In the context of big data, many large-scale knowledge graphs have emerged to effectively organize the explosive growth of web data on the Internet. To select suitable knowledge graphs for use from many knowledge grap...In the context of big data, many large-scale knowledge graphs have emerged to effectively organize the explosive growth of web data on the Internet. To select suitable knowledge graphs for use from many knowledge graphs, quality assessment is particularly important. As an important thing of quality assessment, completeness assessment generally refers to the ratio of the current data volume to the total data volume.When evaluating the completeness of a knowledge graph, it is often necessary to refine the completeness dimension by setting different completeness metrics to produce more complete and understandable evaluation results for the knowledge graph.However, lack of awareness of requirements is the most problematic quality issue. In the actual evaluation process, the existing completeness metrics need to consider the actual application. Therefore, to accurately recommend suitable knowledge graphs to many users, it is particularly important to develop relevant measurement metrics and formulate measurement schemes for completeness. In this paper, we will first clarify the concept of completeness, establish each metric of completeness, and finally design a measurement proposal for the completeness of knowledge graphs.展开更多
Cycle multiplicity of a graph G is the maximum number of edge disjoint cycles in G. In this paper, we determine the cycle multiplicity of and then obtain the formula of cycle multiplicity of total graph of complete bi...Cycle multiplicity of a graph G is the maximum number of edge disjoint cycles in G. In this paper, we determine the cycle multiplicity of and then obtain the formula of cycle multiplicity of total graph of complete bipartite graph, this generalizes the result for, which is given by M.M. Akbar Ali in [1].展开更多
Let G be a simple graph. A total coloring f of G is called an E-total coloring if no two adjacent vertices of G receive the same color, and no edge of G receives the same color as one of its endpoints....Let G be a simple graph. A total coloring f of G is called an E-total coloring if no two adjacent vertices of G receive the same color, and no edge of G receives the same color as one of its endpoints. For an E-total coloring f of a graph G and any vertex x of G, let C(x) denote the set of colors of vertex x and of the edges incident with x, we call C(x) the color set of x. If C(u) ≠ C(v) for any two different vertices u and v of V (G), then we say that f is a vertex-distinguishing E-total coloring of G or a VDET coloring of G for short. The minimum number of colors required for a VDET coloring of G is denoted by Хvt^e(G) and is called the VDE T chromatic number of G. The VDET coloring of complete bipartite graph K7,n (7 ≤ n ≤ 95) is discussed in this paper and the VDET chromatic number of K7,n (7 ≤ n ≤ 95) has been obtained.展开更多
For a simple graph G,let matrix Q(G)=D(G) + A(G) be it's signless Laplacian matrix and Q G (λ)=det(λI Q) it's signless Laplacian characteristic polynomial,where D(G) denotes the diagonal matrix of vertex deg...For a simple graph G,let matrix Q(G)=D(G) + A(G) be it's signless Laplacian matrix and Q G (λ)=det(λI Q) it's signless Laplacian characteristic polynomial,where D(G) denotes the diagonal matrix of vertex degrees of G,A(G) denotes its adjacency matrix of G.If all eigenvalues of Q G (λ) are integral,then the graph G is called Q-integral.In this paper,we obtain that the signless Laplacian characteristic polynomials of the complete multi-partite graphs G=K(n_1,n_2,···,n_t).We prove that the complete t-partite graphs K(n,n,···,n)t are Q-integral and give a necessary and sufficient condition for the complete multipartite graphs K(m,···,m)s(n,···,n)t to be Q-integral.We also obtain that the signless Laplacian characteristic polynomials of the complete multipartite graphs K(m,···,m,)s1(n,···,n,)s2(l,···,l)s3.展开更多
A signed(res. signed total) Roman dominating function, SRDF(res.STRDF) for short, of a graph G =(V, E) is a function f : V → {-1, 1, 2} satisfying the conditions that(i)∑v∈N[v]f(v) ≥ 1(res.∑v∈N(v)f(v) ≥ 1) for ...A signed(res. signed total) Roman dominating function, SRDF(res.STRDF) for short, of a graph G =(V, E) is a function f : V → {-1, 1, 2} satisfying the conditions that(i)∑v∈N[v]f(v) ≥ 1(res.∑v∈N(v)f(v) ≥ 1) for any v ∈ V, where N [v] is the closed neighborhood and N(v) is the neighborhood of v, and(ii) every vertex v for which f(v) =-1 is adjacent to a vertex u for which f(u) = 2. The weight of a SRDF(res. STRDF) is the sum of its function values over all vertices.The signed(res. signed total) Roman domination number of G is the minimum weight among all signed(res. signed total) Roman dominating functions of G. In this paper,we compute the exact values of the signed(res. signed total) Roman domination numbers of complete bipartite graphs and wheels.展开更多
Let G be a simple graph. An IE-total coloring f of G is a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. For each vertex x of G, let C(x) be the set of colors of verte...Let G be a simple graph. An IE-total coloring f of G is a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. For each vertex x of G, let C(x) be the set of colors of vertex x and edges incident to x under f. For an IE-total coloring f of G using k colors, if C(u) ≠ C(v) for any two different vertices u and v of G, then f is called a k-vertex-distinguishing IE-total-coloring of G or a k-VDIET coloring of G for short. The minimum number of colors required for a VDIET coloring of G is denoted by χ_(vt)^(ie) (G) and is called vertex-distinguishing IE-total chromatic number or the VDIET chromatic number of G for short. The VDIET colorings of complete bipartite graphs K_(8,n)are discussed in this paper. Particularly, the VDIET chromatic number of K_(8,n) are obtained.展开更多
Let D(G) =(d_(ij))_(n×n) denote the distance matrix of a connected graph G with order n, where d_(ij) is equal to the distance between vertices viand vjin G. A graph is called distance integral if all eigenvalues...Let D(G) =(d_(ij))_(n×n) denote the distance matrix of a connected graph G with order n, where d_(ij) is equal to the distance between vertices viand vjin G. A graph is called distance integral if all eigenvalues of its distance matrix are integers. In 2014, Yang and Wang gave a sufficient and necessary condition for complete r-partite graphs K_(p1,p2,···,pr)=K_(a1·p1,a2·p2,···,as···ps) to be distance integral and obtained such distance integral graphs with s = 1, 2, 3, 4. However distance integral complete multipartite graphs K_(a1·p1,a2·p2,···,as·ps) with s > 4 have not been found. In this paper, we find and construct some infinite classes of these distance integral graphs K_(a1·p1,a2·p2,···,as·ps) with s = 5, 6. The problem of the existence of such distance integral graphs K_(a1·p1,a2·p2,···,as·ps) with arbitrarily large number s remains open.展开更多
The quantum search on the graph is a very important topic.In this work,we develop a theoretic method on searching of single vertex on the graph[Phys.Rev.Lett.114110503(2015)],and systematically study the search of man...The quantum search on the graph is a very important topic.In this work,we develop a theoretic method on searching of single vertex on the graph[Phys.Rev.Lett.114110503(2015)],and systematically study the search of many vertices on one low-connectivity graph,the joined complete graph.Our results reveal that,with the optimal jumping rate obtained from the theoretical method,we can find such target vertices at the time O(√N),where N is the number of total vertices.Therefore,the search of many vertices on the joined complete graph possessing quantum advantage has been achieved.展开更多
The bondage number of γ f, b f(G) , is defined to be the minimum cardinality of a set of edges whose removal from G results in a graph G′ satisfying γ f(G′)> γ f(G) . The reinforcement number of γ f, ...The bondage number of γ f, b f(G) , is defined to be the minimum cardinality of a set of edges whose removal from G results in a graph G′ satisfying γ f(G′)> γ f(G) . The reinforcement number of γ f, r f(G) , is defined to be the minimum cardinality of a set of edges which when added to G results in a graph G′ satisfying γ f(G′)< γ f(G) . G.S.Domke and R.C.Laskar initiated the study of them and gave exact values of b f(G) and r f(G) for some classes of graphs. Exact values of b f(G) and r f(G) for complete multipartite graphs are given and some results are extended.展开更多
In this paper,a new concept of an optimal complete multipartite decomposition of type 1 (type 2) of a complete n-partite graph Q n is proposed and another new concept of a normal complete multipartite decomposition o...In this paper,a new concept of an optimal complete multipartite decomposition of type 1 (type 2) of a complete n-partite graph Q n is proposed and another new concept of a normal complete multipartite decomposition of K n is introduced.It is showed that an optimal complete multipartite decomposition of type 1 of K n is a normal complete multipartite decomposition.As for any complete multipartite decomposition of K n,there is a derived complete multipartite decomposition for Q n.It is also showed that any optimal complete multipartite decomposition of type 1 of Q n is a derived decomposition of an optimal complete multipartite decomposition of type 1 of K n.Besides,some structural properties of an optimal complete multipartite decomposition of type 1 of K n are given.展开更多
<div style="text-align:justify;"> <span style="font-family:Verdana;">In the field of design theory, the most well-known design is a Steiner Triple System. In general, a G-design on H is...<div style="text-align:justify;"> <span style="font-family:Verdana;">In the field of design theory, the most well-known design is a Steiner Triple System. In general, a G-design on H is an edge-disjoint decomposition of H into isomorphic copies of G. In a Steiner Triple system, a complete graph is decomposed into triangles. In this paper we let H be a complete graph with a hole and G be a complete graph on four vertices minus one edge, also referred to as a <img alt="" src="Edit_e69ee166-4bbc-48f5-8ba1-b446e7d3738c.png" /> . A complete graph with a hole, <img alt="" src="Edit_558c249b-55e8-4f3b-a043-e36d001c4250.png" />, consists of a complete graph on <em>d</em> vertices, <img alt="" src="Edit_cb1772f7-837c-4aea-b4a6-cb38565f5a8b.png" />, and a set of independent vertices of size<em> v, V,</em> where each vertex in <em>V</em> is adjacent to each vertex in <img alt="" src="Edit_cb1772f7-837c-4aea-b4a6-cb38565f5a8b.png" />. When <em>d</em> is even, we give two constructions for the decomposition of a complete graph with a hole into copies of <img alt="" src="Edit_e69ee166-4bbc-48f5-8ba1-b446e7d3738c.png" /> : the Alpha-Delta Construction, and the Alpha-Beta-Delta Construction. By restricting <em>d</em> and <em>v</em> so that <img alt="" src="Edit_6bb9e3b4-1769-4b28-bf89-bc97c47c637e.png" /><span style="white-space:nowrap;"> </span>, we are able to resolve both of these cases for a subset of <img alt="" src="Edit_558c249b-55e8-4f3b-a043-e36d001c4250.png" />using difference methods and 1-factors.</span> </div>展开更多
Characterizing regular covers of symmetric graphs is one of the fundamental topics in the field of algebraic graph theory, and is often a key step for approaching general symmetric graphs. Complete graphs, which are t...Characterizing regular covers of symmetric graphs is one of the fundamental topics in the field of algebraic graph theory, and is often a key step for approaching general symmetric graphs. Complete graphs, which are typical symmetric graphs, naturally appear in the study of many symmetric graphs as normal quotient graphs. In this paper, a characterization of edge-transitive cyclic covers of complete graphs with prime power order is given by using the techniques of finite group theory and the related properties of coset graphs. Certain previous results are generalized and some new families of examples are founded.展开更多
A packing of the complete directed symmetric graph DK v with m circuits, denoted by ( v,m) DCP, is defined to be a family of arc disjoint m circuits of DK v such that any one arc of DK v \ occurs...A packing of the complete directed symmetric graph DK v with m circuits, denoted by ( v,m) DCP, is defined to be a family of arc disjoint m circuits of DK v such that any one arc of DK v \ occurs in at most one m circuit. The packing number P(v,m) is the maximum number of m circuits in such a packing. The packing problem is to determine the value P(v,m) for every integer v≥m. In this paper, the problem is reduced to the case m+6≤v≤2m- 4m-3+12 , for any fixed even integer m≥4 . In particular, the values of P(v,m) are completely determined for m=12 , 14 and 16.展开更多
Aquatic medicine knowledge graph is an effective means to realize intelligent aquaculture.Graph completion technology is key to improving the quality of knowledge graph construction.However,the difficulty of semantic ...Aquatic medicine knowledge graph is an effective means to realize intelligent aquaculture.Graph completion technology is key to improving the quality of knowledge graph construction.However,the difficulty of semantic discrimination among similar entities and inconspicuous semantic features result in low accuracy when completing aquatic medicine knowledge graph with complex relationships.In this study,an aquatic medicine knowledge graph completion method(TransH+HConvAM)is proposed.Firstly,TransH is applied to split the vector plane between entities and relations,ameliorating the poor completion effect caused by low semantic resolution of entities.Then,hybrid convolution is introduced to obtain the global interaction of triples based on the complete interaction between head/tail entities and relations,which improves the semantic features of triples and enhances the completion effect of complex relationships in the graph.Experiments are conducted to verify the performance of the proposed method.The MR,MRR and Hit@10 of the TransH+HConvAM are found to be 674,0.339,and 0.361,respectively.This study shows that the model effectively overcomes the poor completion effect of complex relationships and improves the construction quality of the aquatic medicine knowledge graph,providing technical support for intelligent aquaculture.展开更多
Knowledge graph(KG) link prediction aims to address the problem of missing multiple valid triples in KGs. Existing approaches either struggle to efficiently model the message passing process of multi-hop paths or lack...Knowledge graph(KG) link prediction aims to address the problem of missing multiple valid triples in KGs. Existing approaches either struggle to efficiently model the message passing process of multi-hop paths or lack transparency of model prediction principles. In this paper,a new graph convolutional network path semantic-aware graph convolution network(PSGCN) is proposed to achieve modeling the semantic information of multi-hop paths. PSGCN first uses a random walk strategy to obtain all-hop paths in KGs,then captures the semantics of the paths by Word2Sec and long shortterm memory(LSTM) models,and finally converts them into a potential representation for the graph convolution network(GCN) messaging process. PSGCN combines path-based inference methods and graph neural networks to achieve better interpretability and scalability. In addition,to ensure the robustness of the model,the value of the path thresholdKis experimented on the FB15K-237 and WN18RR datasets,and the final results prove the effectiveness of the model.展开更多
To solve the problem of missing many valid triples in knowledge graphs(KGs),a novel model based on a convolutional neural network(CNN)called ConvKG is proposed,which employs a joint learning strategy for knowledge gra...To solve the problem of missing many valid triples in knowledge graphs(KGs),a novel model based on a convolutional neural network(CNN)called ConvKG is proposed,which employs a joint learning strategy for knowledge graph completion(KGC).Related research work has shown the superiority of convolutional neural networks(CNNs)in extracting semantic features of triple embeddings.However,these researches use only one single-shaped filter and fail to extract semantic features of different granularity.To solve this problem,ConvKG exploits multi-shaped filters to co-convolute on the triple embeddings,joint learning semantic features of different granularity.Different shaped filters cover different sizes on the triple embeddings and capture pairwise interactions of different granularity among triple elements.Experimental results confirm the strength of joint learning,and compared with state-of-the-art CNN-based KGC models,ConvKG achieves the better mean rank(MR)and Hits@10 metrics on dataset WN18 RR,and the better MR on dataset FB15k-237.展开更多
Let G = (V,E) be a simple graph without isolated vertices. For positive integer k, a 3-valued function f : V → {-1,0,1} is said to be a minus total k-subdominating function (MTkSF) if sum from (u∈N(v)) to f(u)≥1 fo...Let G = (V,E) be a simple graph without isolated vertices. For positive integer k, a 3-valued function f : V → {-1,0,1} is said to be a minus total k-subdominating function (MTkSF) if sum from (u∈N(v)) to f(u)≥1 for at least k vertices v in G, where N(v) is the open neighborhood of v. The minus total k-subdomination number γkt(G) equals the minimum weight of an MTkSF on G. In this paper, the values on the minus total k-subdomination number of some special graphs are investigated. Several lower bounds on γkt of general graphs and trees are obtained.展开更多
We introduce the triple crossing number, a variation of the crossing number, of a graph, which is the minimal number of crossing points in all drawings of the graph with only triple crossings. It is defined to be zero...We introduce the triple crossing number, a variation of the crossing number, of a graph, which is the minimal number of crossing points in all drawings of the graph with only triple crossings. It is defined to be zero for planar graphs, and to be infinite for non-planar graphs which do not admit a drawing with only triple crossings. In this paper, we determine the triple crossing numbers for all complete multipartite graphs which include all complete graphs.展开更多
The interval graph completion problem on a graph G is to find an added edge set F such that G + F is an interval supergraph with the smallest possible number of edges. The problem has important applications to numeric...The interval graph completion problem on a graph G is to find an added edge set F such that G + F is an interval supergraph with the smallest possible number of edges. The problem has important applications to numerical algebra, V LSI-layout and algorithm graph theory etc; And it has been known to be N P-complete on general graphs. Some classes of special graphs have been investigated in the literatures. In this paper the interval graph completion problem on split graphs is investigated.展开更多
This article presents an optimized approach of mathematical techniques in themedical domain by manoeuvring the phenomenon of ant colony optimization algorithm(also known as ACO).A complete graph of blood banks and a p...This article presents an optimized approach of mathematical techniques in themedical domain by manoeuvring the phenomenon of ant colony optimization algorithm(also known as ACO).A complete graph of blood banks and a path that covers all the blood banks without repeating any link is required by applying the Travelling Salesman Problem(often TSP).The wide use promises to accelerate and offers the opportunity to cultivate health care,particularly in remote or unmerited environments by shrinking lab testing reversal times,empowering just-in-time lifesaving medical supply.展开更多
基金supported by the National Key Laboratory for Comp lex Systems Simulation Foundation (6142006190301)。
文摘In the context of big data, many large-scale knowledge graphs have emerged to effectively organize the explosive growth of web data on the Internet. To select suitable knowledge graphs for use from many knowledge graphs, quality assessment is particularly important. As an important thing of quality assessment, completeness assessment generally refers to the ratio of the current data volume to the total data volume.When evaluating the completeness of a knowledge graph, it is often necessary to refine the completeness dimension by setting different completeness metrics to produce more complete and understandable evaluation results for the knowledge graph.However, lack of awareness of requirements is the most problematic quality issue. In the actual evaluation process, the existing completeness metrics need to consider the actual application. Therefore, to accurately recommend suitable knowledge graphs to many users, it is particularly important to develop relevant measurement metrics and formulate measurement schemes for completeness. In this paper, we will first clarify the concept of completeness, establish each metric of completeness, and finally design a measurement proposal for the completeness of knowledge graphs.
文摘Cycle multiplicity of a graph G is the maximum number of edge disjoint cycles in G. In this paper, we determine the cycle multiplicity of and then obtain the formula of cycle multiplicity of total graph of complete bipartite graph, this generalizes the result for, which is given by M.M. Akbar Ali in [1].
文摘Let G be a simple graph. A total coloring f of G is called an E-total coloring if no two adjacent vertices of G receive the same color, and no edge of G receives the same color as one of its endpoints. For an E-total coloring f of a graph G and any vertex x of G, let C(x) denote the set of colors of vertex x and of the edges incident with x, we call C(x) the color set of x. If C(u) ≠ C(v) for any two different vertices u and v of V (G), then we say that f is a vertex-distinguishing E-total coloring of G or a VDET coloring of G for short. The minimum number of colors required for a VDET coloring of G is denoted by Хvt^e(G) and is called the VDE T chromatic number of G. The VDET coloring of complete bipartite graph K7,n (7 ≤ n ≤ 95) is discussed in this paper and the VDET chromatic number of K7,n (7 ≤ n ≤ 95) has been obtained.
基金Supported by the NSFC(60863006)Supported by the NCET(-06-0912)Supported by the Science-Technology Foundation for Middle-aged and Yong Scientist of Qinghai University(2011-QGY-8)
文摘For a simple graph G,let matrix Q(G)=D(G) + A(G) be it's signless Laplacian matrix and Q G (λ)=det(λI Q) it's signless Laplacian characteristic polynomial,where D(G) denotes the diagonal matrix of vertex degrees of G,A(G) denotes its adjacency matrix of G.If all eigenvalues of Q G (λ) are integral,then the graph G is called Q-integral.In this paper,we obtain that the signless Laplacian characteristic polynomials of the complete multi-partite graphs G=K(n_1,n_2,···,n_t).We prove that the complete t-partite graphs K(n,n,···,n)t are Q-integral and give a necessary and sufficient condition for the complete multipartite graphs K(m,···,m)s(n,···,n)t to be Q-integral.We also obtain that the signless Laplacian characteristic polynomials of the complete multipartite graphs K(m,···,m,)s1(n,···,n,)s2(l,···,l)s3.
基金The NSF(11271365)of Chinathe NSF(BK20151117)of Jiangsu Province
文摘A signed(res. signed total) Roman dominating function, SRDF(res.STRDF) for short, of a graph G =(V, E) is a function f : V → {-1, 1, 2} satisfying the conditions that(i)∑v∈N[v]f(v) ≥ 1(res.∑v∈N(v)f(v) ≥ 1) for any v ∈ V, where N [v] is the closed neighborhood and N(v) is the neighborhood of v, and(ii) every vertex v for which f(v) =-1 is adjacent to a vertex u for which f(u) = 2. The weight of a SRDF(res. STRDF) is the sum of its function values over all vertices.The signed(res. signed total) Roman domination number of G is the minimum weight among all signed(res. signed total) Roman dominating functions of G. In this paper,we compute the exact values of the signed(res. signed total) Roman domination numbers of complete bipartite graphs and wheels.
基金Supported by the National Natural Science Foundation of China(61163037, 61163054, 11261046, 61363060)
文摘Let G be a simple graph. An IE-total coloring f of G is a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. For each vertex x of G, let C(x) be the set of colors of vertex x and edges incident to x under f. For an IE-total coloring f of G using k colors, if C(u) ≠ C(v) for any two different vertices u and v of G, then f is called a k-vertex-distinguishing IE-total-coloring of G or a k-VDIET coloring of G for short. The minimum number of colors required for a VDIET coloring of G is denoted by χ_(vt)^(ie) (G) and is called vertex-distinguishing IE-total chromatic number or the VDIET chromatic number of G for short. The VDIET colorings of complete bipartite graphs K_(8,n)are discussed in this paper. Particularly, the VDIET chromatic number of K_(8,n) are obtained.
基金Supported by the National Natural Science Foundation of China(11171273) Supported by the Graduate Starting Seed Fund of Northwestern Polytechnical University(Z2014173)
文摘Let D(G) =(d_(ij))_(n×n) denote the distance matrix of a connected graph G with order n, where d_(ij) is equal to the distance between vertices viand vjin G. A graph is called distance integral if all eigenvalues of its distance matrix are integers. In 2014, Yang and Wang gave a sufficient and necessary condition for complete r-partite graphs K_(p1,p2,···,pr)=K_(a1·p1,a2·p2,···,as···ps) to be distance integral and obtained such distance integral graphs with s = 1, 2, 3, 4. However distance integral complete multipartite graphs K_(a1·p1,a2·p2,···,as·ps) with s > 4 have not been found. In this paper, we find and construct some infinite classes of these distance integral graphs K_(a1·p1,a2·p2,···,as·ps) with s = 5, 6. The problem of the existence of such distance integral graphs K_(a1·p1,a2·p2,···,as·ps) with arbitrarily large number s remains open.
基金the National Key R&D Program of China(Grant No.2017YFA0303800)the National Natural Science Foundation of China(Grant Nos.91850205 and 11974046)。
文摘The quantum search on the graph is a very important topic.In this work,we develop a theoretic method on searching of single vertex on the graph[Phys.Rev.Lett.114110503(2015)],and systematically study the search of many vertices on one low-connectivity graph,the joined complete graph.Our results reveal that,with the optimal jumping rate obtained from the theoretical method,we can find such target vertices at the time O(√N),where N is the number of total vertices.Therefore,the search of many vertices on the joined complete graph possessing quantum advantage has been achieved.
文摘The bondage number of γ f, b f(G) , is defined to be the minimum cardinality of a set of edges whose removal from G results in a graph G′ satisfying γ f(G′)> γ f(G) . The reinforcement number of γ f, r f(G) , is defined to be the minimum cardinality of a set of edges which when added to G results in a graph G′ satisfying γ f(G′)< γ f(G) . G.S.Domke and R.C.Laskar initiated the study of them and gave exact values of b f(G) and r f(G) for some classes of graphs. Exact values of b f(G) and r f(G) for complete multipartite graphs are given and some results are extended.
基金Supported by the National Natural Science Foundation of China( 1 0 2 71 1 1 0 )
文摘In this paper,a new concept of an optimal complete multipartite decomposition of type 1 (type 2) of a complete n-partite graph Q n is proposed and another new concept of a normal complete multipartite decomposition of K n is introduced.It is showed that an optimal complete multipartite decomposition of type 1 of K n is a normal complete multipartite decomposition.As for any complete multipartite decomposition of K n,there is a derived complete multipartite decomposition for Q n.It is also showed that any optimal complete multipartite decomposition of type 1 of Q n is a derived decomposition of an optimal complete multipartite decomposition of type 1 of K n.Besides,some structural properties of an optimal complete multipartite decomposition of type 1 of K n are given.
文摘<div style="text-align:justify;"> <span style="font-family:Verdana;">In the field of design theory, the most well-known design is a Steiner Triple System. In general, a G-design on H is an edge-disjoint decomposition of H into isomorphic copies of G. In a Steiner Triple system, a complete graph is decomposed into triangles. In this paper we let H be a complete graph with a hole and G be a complete graph on four vertices minus one edge, also referred to as a <img alt="" src="Edit_e69ee166-4bbc-48f5-8ba1-b446e7d3738c.png" /> . A complete graph with a hole, <img alt="" src="Edit_558c249b-55e8-4f3b-a043-e36d001c4250.png" />, consists of a complete graph on <em>d</em> vertices, <img alt="" src="Edit_cb1772f7-837c-4aea-b4a6-cb38565f5a8b.png" />, and a set of independent vertices of size<em> v, V,</em> where each vertex in <em>V</em> is adjacent to each vertex in <img alt="" src="Edit_cb1772f7-837c-4aea-b4a6-cb38565f5a8b.png" />. When <em>d</em> is even, we give two constructions for the decomposition of a complete graph with a hole into copies of <img alt="" src="Edit_e69ee166-4bbc-48f5-8ba1-b446e7d3738c.png" /> : the Alpha-Delta Construction, and the Alpha-Beta-Delta Construction. By restricting <em>d</em> and <em>v</em> so that <img alt="" src="Edit_6bb9e3b4-1769-4b28-bf89-bc97c47c637e.png" /><span style="white-space:nowrap;"> </span>, we are able to resolve both of these cases for a subset of <img alt="" src="Edit_558c249b-55e8-4f3b-a043-e36d001c4250.png" />using difference methods and 1-factors.</span> </div>
文摘Characterizing regular covers of symmetric graphs is one of the fundamental topics in the field of algebraic graph theory, and is often a key step for approaching general symmetric graphs. Complete graphs, which are typical symmetric graphs, naturally appear in the study of many symmetric graphs as normal quotient graphs. In this paper, a characterization of edge-transitive cyclic covers of complete graphs with prime power order is given by using the techniques of finite group theory and the related properties of coset graphs. Certain previous results are generalized and some new families of examples are founded.
文摘A packing of the complete directed symmetric graph DK v with m circuits, denoted by ( v,m) DCP, is defined to be a family of arc disjoint m circuits of DK v such that any one arc of DK v \ occurs in at most one m circuit. The packing number P(v,m) is the maximum number of m circuits in such a packing. The packing problem is to determine the value P(v,m) for every integer v≥m. In this paper, the problem is reduced to the case m+6≤v≤2m- 4m-3+12 , for any fixed even integer m≥4 . In particular, the values of P(v,m) are completely determined for m=12 , 14 and 16.
基金supported by the Key Laboratory of Environment Controlled Aquaculture(Dalian Ocean University)Ministry of Education(No.2021-MOEKLECA-KF-05)the National Natural Science Foundation of China Youth Science(No.61802046)。
文摘Aquatic medicine knowledge graph is an effective means to realize intelligent aquaculture.Graph completion technology is key to improving the quality of knowledge graph construction.However,the difficulty of semantic discrimination among similar entities and inconspicuous semantic features result in low accuracy when completing aquatic medicine knowledge graph with complex relationships.In this study,an aquatic medicine knowledge graph completion method(TransH+HConvAM)is proposed.Firstly,TransH is applied to split the vector plane between entities and relations,ameliorating the poor completion effect caused by low semantic resolution of entities.Then,hybrid convolution is introduced to obtain the global interaction of triples based on the complete interaction between head/tail entities and relations,which improves the semantic features of triples and enhances the completion effect of complex relationships in the graph.Experiments are conducted to verify the performance of the proposed method.The MR,MRR and Hit@10 of the TransH+HConvAM are found to be 674,0.339,and 0.361,respectively.This study shows that the model effectively overcomes the poor completion effect of complex relationships and improves the construction quality of the aquatic medicine knowledge graph,providing technical support for intelligent aquaculture.
基金Supported by the National Natural Science Foundation of China(No.61876144).
文摘Knowledge graph(KG) link prediction aims to address the problem of missing multiple valid triples in KGs. Existing approaches either struggle to efficiently model the message passing process of multi-hop paths or lack transparency of model prediction principles. In this paper,a new graph convolutional network path semantic-aware graph convolution network(PSGCN) is proposed to achieve modeling the semantic information of multi-hop paths. PSGCN first uses a random walk strategy to obtain all-hop paths in KGs,then captures the semantics of the paths by Word2Sec and long shortterm memory(LSTM) models,and finally converts them into a potential representation for the graph convolution network(GCN) messaging process. PSGCN combines path-based inference methods and graph neural networks to achieve better interpretability and scalability. In addition,to ensure the robustness of the model,the value of the path thresholdKis experimented on the FB15K-237 and WN18RR datasets,and the final results prove the effectiveness of the model.
基金Supported by the National Natural Science Foundation of China(No.61876144)。
文摘To solve the problem of missing many valid triples in knowledge graphs(KGs),a novel model based on a convolutional neural network(CNN)called ConvKG is proposed,which employs a joint learning strategy for knowledge graph completion(KGC).Related research work has shown the superiority of convolutional neural networks(CNNs)in extracting semantic features of triple embeddings.However,these researches use only one single-shaped filter and fail to extract semantic features of different granularity.To solve this problem,ConvKG exploits multi-shaped filters to co-convolute on the triple embeddings,joint learning semantic features of different granularity.Different shaped filters cover different sizes on the triple embeddings and capture pairwise interactions of different granularity among triple elements.Experimental results confirm the strength of joint learning,and compared with state-of-the-art CNN-based KGC models,ConvKG achieves the better mean rank(MR)and Hits@10 metrics on dataset WN18 RR,and the better MR on dataset FB15k-237.
基金supported by the National Natural Science Foundation of China (Grant No.10571117)the Development Foundation of Shanghai Municipal Education Commission (Grant No.05AZ04)
文摘Let G = (V,E) be a simple graph without isolated vertices. For positive integer k, a 3-valued function f : V → {-1,0,1} is said to be a minus total k-subdominating function (MTkSF) if sum from (u∈N(v)) to f(u)≥1 for at least k vertices v in G, where N(v) is the open neighborhood of v. The minus total k-subdomination number γkt(G) equals the minimum weight of an MTkSF on G. In this paper, the values on the minus total k-subdomination number of some special graphs are investigated. Several lower bounds on γkt of general graphs and trees are obtained.
文摘We introduce the triple crossing number, a variation of the crossing number, of a graph, which is the minimal number of crossing points in all drawings of the graph with only triple crossings. It is defined to be zero for planar graphs, and to be infinite for non-planar graphs which do not admit a drawing with only triple crossings. In this paper, we determine the triple crossing numbers for all complete multipartite graphs which include all complete graphs.
基金Supported by the National Natural Science Foundation of China(11101383) Supported by the Natural Science Foundation of Henan Province(112300410047)
文摘The interval graph completion problem on a graph G is to find an added edge set F such that G + F is an interval supergraph with the smallest possible number of edges. The problem has important applications to numerical algebra, V LSI-layout and algorithm graph theory etc; And it has been known to be N P-complete on general graphs. Some classes of special graphs have been investigated in the literatures. In this paper the interval graph completion problem on split graphs is investigated.
文摘This article presents an optimized approach of mathematical techniques in themedical domain by manoeuvring the phenomenon of ant colony optimization algorithm(also known as ACO).A complete graph of blood banks and a path that covers all the blood banks without repeating any link is required by applying the Travelling Salesman Problem(often TSP).The wide use promises to accelerate and offers the opportunity to cultivate health care,particularly in remote or unmerited environments by shrinking lab testing reversal times,empowering just-in-time lifesaving medical supply.