A function f: V( G)→{1,1} defined on the vertices of a graph G is a signed total dominating function (STDF) if the sum of its function values over any open neighborhood is at least one. An STDF f is minimal if t...A function f: V( G)→{1,1} defined on the vertices of a graph G is a signed total dominating function (STDF) if the sum of its function values over any open neighborhood is at least one. An STDF f is minimal if there does not extst a STDF g: V(G)→{-1,1}, f≠g, for which g ( v )≤f( v ) for every v∈V( G ). The weight of a STDF is the sum of its function values over all vertices. The signed total domination number of G is the minimum weight of a STDF of G, while the upper signed domination number of G is the maximum weight of a minimal STDF of G, In this paper, we present sharp upper bounds on the upper signed total domination number of a nearly regular graph.展开更多
Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs(SRGs) with parameters(N, k, λ, μ) achieves full quantum speedup. The problem is reconsidered ...Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs(SRGs) with parameters(N, k, λ, μ) achieves full quantum speedup. The problem is reconsidered in terms of scattering quantum walk, a type of discrete-time quantum walks. Here, the search space is confined to a low-dimensional subspace corresponding to the collapsed graph of SRGs. To quantify the algorithm's performance, we leverage the fundamental pairing theorem, a general theory developed by Cottrell for quantum search of structural anomalies in star graphs.The search algorithm on the SRGs with k scales as N satisfies the theorem, and results can be immediately obtained, while search on the SRGs with k scales as√N does not satisfy the theorem, and matrix perturbation theory is used to provide an analysis. Both these cases can be solved in O(√N) time steps with a success probability close to 1. The analytical conclusions are verified by simulation results on two SRGs. These examples show that the formalism on star graphs can be applied more generally.展开更多
A generalized strongly regular graphof grade p,as anew generalization of strongly regular graphs,is a regular graph such that the number of common neighbours of both any two adjacent vertices and any two non-adjacent ...A generalized strongly regular graphof grade p,as anew generalization of strongly regular graphs,is a regular graph such that the number of common neighbours of both any two adjacent vertices and any two non-adjacent vertices takes on p distinct values.For any vertex u of a generalized strongly regular graph of grade 2 with parameters(n,k;a_(1),a_(2);c_(1),c_(2)),if the number of the vertices that are adjacent to u and share ai(i=1,2)common neighbours with u,or are non-adjacent to u and share c,(i=1,2)common neighbours with is independent of the choice of the vertex u,then the generalized strongly regular graph of grade 2 is free.In this paper,we investigate the generalized strongly regular graph of grade 2 with parameters(n,k;k-1,a_(2);k-1,c_(2))and provide the sufficient and necessary conditions for the existence of a family of free generalized strongly regular graphs of grade 2.展开更多
Fault diagnosis is an important area of study with regard to the design and maintenance of multiprocessor systems.A new measure for fault diagnosis of systems,namely,non-inclusive diagnosability(denoted by MM^(*)),was...Fault diagnosis is an important area of study with regard to the design and maintenance of multiprocessor systems.A new measure for fault diagnosis of systems,namely,non-inclusive diagnosability(denoted by MM^(*)),was proposed by Ding et al.In this paper,we establish the non-inclusive diagnosability of a class of regular graphs under the PMC model and the MM^(*)model.As applications,the non-inclusive diagnosabilities of hypercubes,hierarchical hypercubes,folded hypercubes,star graphs,bubble-sort graphs,pancake graphs and dual cubes are determined under the PMC model and the[Math Processing Error]model.展开更多
The goal of the present paper is to provide a gallery of small directed strongly regular graphs.For each graph of order n≤12 and valency k<n/2,a diagram is depicted,its relation to other small directed strongly re...The goal of the present paper is to provide a gallery of small directed strongly regular graphs.For each graph of order n≤12 and valency k<n/2,a diagram is depicted,its relation to other small directed strongly regular graphs is revealed,the full group of automorphisms is described,and some other nice properties are given.To each graph a list of interesting subgraphs is provided as well.展开更多
An(s,t)-partition of a graph G=(V,E)is a partition of V=V 1∪V 2 suchthatδ(G[V_(1)])≥s andδ(G[V_(2)])≥t.Ithasbeenconjecturedthat,forsufficiently large n,every d-regular graph of order n has a(d/2,d/2)-partition(ca...An(s,t)-partition of a graph G=(V,E)is a partition of V=V 1∪V 2 suchthatδ(G[V_(1)])≥s andδ(G[V_(2)])≥t.Ithasbeenconjecturedthat,forsufficiently large n,every d-regular graph of order n has a(d/2,d/2)-partition(called an internal partition).Inthispaper,weprovethateveryd-regulargraphofordern hasa(d/2,d/2)partition(called a weak internal partition)for d≤9 and sufficiently large n.展开更多
Plesnik in 1972 proved that an (m - 1)-edge connected m-regular graph of even order has a 1-factor containing any given edge and has another 1-factor excluding any given m - 1 edges. Alder et al. in 1999 showed that...Plesnik in 1972 proved that an (m - 1)-edge connected m-regular graph of even order has a 1-factor containing any given edge and has another 1-factor excluding any given m - 1 edges. Alder et al. in 1999 showed that if G is a regular (2n + 1)-edge-connected bipartite graph, then G has a 1-factor containing any given edge and excluding any given matching of size n. In this paper we obtain some sufficient conditions related to the edge-connectivity for an n-regular graph to have a k-factor containing a set of edges and (or) excluding a set of edges, where 1 ≤ k ≤n/2. In particular, we generalize Plesnik's result and the results obtained by Liu et al. in 1998, and improve Katerinis' result obtained 1993. Furthermore, we show that the results in this paper are the best possible.展开更多
For any even integer k and any integer i, we prove that a (kr +i)-regular multigraph contains a k-factor if it contains no more than kr - 3k/2+ i + 2 cut edges, and this result is the best possible to guarantee t...For any even integer k and any integer i, we prove that a (kr +i)-regular multigraph contains a k-factor if it contains no more than kr - 3k/2+ i + 2 cut edges, and this result is the best possible to guarantee the existence of k-factor in terms of the number of cut edges. We further give a characterization for k-factor free regular graphs.展开更多
A graph G is k-covered if each edge of G belongs to a k-factor of G. We determine some valuee of k for which every r-regular graph with edge-connectivity λ is k-covered.
Let G = (V, E) be a finite, simple and undirected graph with p vertices and q edges. An (a, d)-vertex-antimagic total labeling of G is a bijection f from V(G) t2 E(G) onto the set of consecutive integers 1, 2,...Let G = (V, E) be a finite, simple and undirected graph with p vertices and q edges. An (a, d)-vertex-antimagic total labeling of G is a bijection f from V(G) t2 E(G) onto the set of consecutive integers 1, 2,... ,p + q, such that the vertex-weights form an arithmetic progression with the initial term a and difference d, where the vertex-weight of x is the sum of the value f(x) assigned to the vertex x together with all values f(xy) assigned to edges xy incident to x. Such labeling is called super if the smallest possible labels appear on the vertices. In this paper, we study the properties of such labelings and examine their existence for 2r-regular graphs when the difference d is 0, 1,..., r + 1.展开更多
Let Гt-(G) be upper minus total domination number of G. In this paper, We establish an upper bound of the upper minus total domination number of a regular graph G and characterize the extremal graphs attaining the ...Let Гt-(G) be upper minus total domination number of G. In this paper, We establish an upper bound of the upper minus total domination number of a regular graph G and characterize the extremal graphs attaining the bound. Thus, we answer an open problem by Yan, Yang and Shan展开更多
The definition of the ascending subgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular...The definition of the ascending subgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular graphs under some conditions do have an ascending subgraph decomposition.展开更多
We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility c...We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility conditions are deduced. Furthermore, we establish some relations between the classical Krein parameters and the generalized Krein parameters.展开更多
In this paper, an equivalent condition of a graph G with t (2≤ t ≤n) distinct Laplacian eigenvalues is established. By applying this condition to t = 3, if G is regular (necessarily be strongly regular), an equi...In this paper, an equivalent condition of a graph G with t (2≤ t ≤n) distinct Laplacian eigenvalues is established. By applying this condition to t = 3, if G is regular (necessarily be strongly regular), an equivalent condition of G being Laplacian integral is given. Also for the case of t = 3, if G is non-regular, it is found that G has diameter 2 and girth at most 5 if G is not a tree. Graph G is characterized in the case of its being triangle-free, bipartite and pentagon-free. In both cases, G is Laplacian integral.展开更多
Currently,functional connectomes constructed from neuroimaging data have emerged as a powerful tool in identifying brain disorders.If one brain disease just manifests as some cognitive dysfunction,it means that the di...Currently,functional connectomes constructed from neuroimaging data have emerged as a powerful tool in identifying brain disorders.If one brain disease just manifests as some cognitive dysfunction,it means that the disease may affect some local connectivity in the brain functional network.That is,there are functional abnormalities in the sub-network.Therefore,it is crucial to accurately identify them in pathological diagnosis.To solve these problems,we proposed a sub-network extraction method based on graph regularization nonnegative matrix factorization(GNMF).The dynamic functional networks of normal subjects and early mild cognitive impairment(eMCI)subjects were vectorized and the functional connection vectors(FCV)were assembled to aggregation matrices.Then GNMF was applied to factorize the aggregation matrix to get the base matrix,in which the column vectors were restored to a common sub-network and a distinctive sub-network,and visualization and statistical analysis were conducted on the two sub-networks,respectively.Experimental results demonstrated that,compared with other matrix factorization methods,the proposed method can more obviously reflect the similarity between the common subnetwork of eMCI subjects and normal subjects,as well as the difference between the distinctive sub-network of eMCI subjects and normal subjects,Therefore,the high-dimensional features in brain functional networks can be best represented locally in the lowdimensional space,which provides a new idea for studying brain functional connectomes.展开更多
The imaging speed is a bottleneck for magnetic resonance imaging( MRI) since it appears. To alleviate this difficulty,a novel graph regularized sparse coding method for highly undersampled MRI reconstruction( GSCMRI) ...The imaging speed is a bottleneck for magnetic resonance imaging( MRI) since it appears. To alleviate this difficulty,a novel graph regularized sparse coding method for highly undersampled MRI reconstruction( GSCMRI) was proposed. The graph regularized sparse coding showed the potential in maintaining the geometrical information of the data. In this study, it was incorporated with two-level Bregman iterative procedure that updated the data term in outer-level and learned dictionary in innerlevel. Moreover,the graph regularized sparse coding and simple dictionary updating stages derived by the inner minimization made the proposed algorithm converge in few iterations, meanwhile achieving superior reconstruction performance. Extensive experimental results have demonstrated GSCMRI can consistently recover both real-valued MR images and complex-valued MR data efficiently,and outperform the current state-of-the-art approaches in terms of higher PSNR and lower HFEN values.展开更多
A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant A such that the equality λd(ui) = ∑(vi,vj)∈E(G) d(vj) holds for all i = 1, 2,…, |V(G)|, where d(vi) denotes the degr...A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant A such that the equality λd(ui) = ∑(vi,vj)∈E(G) d(vj) holds for all i = 1, 2,…, |V(G)|, where d(vi) denotes the degree of vertex vi. In this paper, some harmonic properties of the complement and line graph are given, and some algebraic properties for the λ-Hgraphs are obtained.展开更多
Let LE(G) denote the Laplacian energy of a graph G. In this paper the xyz-transformations G^(xyz) of an r-regular graph G for x,y,z∈{0,1, +,-} are considered. The explicit formulas of LE(G^(xyz)) are presented in ter...Let LE(G) denote the Laplacian energy of a graph G. In this paper the xyz-transformations G^(xyz) of an r-regular graph G for x,y,z∈{0,1, +,-} are considered. The explicit formulas of LE(G^(xyz)) are presented in terms of r,the number of vertices of G for any positive integer r and x,y,z∈{ 0,1},and also for r = 2 and all x,y,z∈{0,1,+,-}. Some Laplacian equienergetic pairs of G^(xyz) for r = 2 and x,y,z∈{0,1, +,-} are obtained. This also provides several ways to construct infinitely many pairs of Laplacian equienergetic graphs.展开更多
Link prediction has attracted wide attention among interdisciplinaryresearchers as an important issue in complex network. It aims to predict the missing links in current networks and new links that will appear in fut...Link prediction has attracted wide attention among interdisciplinaryresearchers as an important issue in complex network. It aims to predict the missing links in current networks and new links that will appear in future networks.Despite the presence of missing links in the target network of link prediction studies, the network it processes remains macroscopically as a large connectedgraph. However, the complexity of the real world makes the complex networksabstracted from real systems often contain many isolated nodes. This phenomenon leads to existing link prediction methods not to efficiently implement the prediction of missing edges on isolated nodes. Therefore, the cold-start linkprediction is favored as one of the most valuable subproblems of traditional linkprediction. However, due to the loss of many links in the observation network, thetopological information available for completing the link prediction task is extremely scarce. This presents a severe challenge for the study of cold-start link prediction. Therefore, how to mine and fuse more available non-topologicalinformation from observed network becomes the key point to solve the problemof cold-start link prediction. In this paper, we propose a framework for solving thecold-start link prediction problem, a joint-weighted symmetric nonnegative matrixfactorization model fusing graph regularization information, based on low-rankapproximation algorithms in the field of machine learning. First, the nonlinear features in high-dimensional space of node attributes are captured by the designedgraph regularization term. Second, using a weighted matrix, we associate the attribute similarity and first order structure information of nodes and constrain eachother. Finally, a unified framework for implementing cold-start link prediction isconstructed by using a symmetric nonnegative matrix factorization model to integrate the multiple information extracted together. Extensive experimental validationon five real networks with attributes shows that the proposed model has very goodpredictive performance when predicting missing edges of isolated nodes.展开更多
Let G be a graph of order n andμbe an adjacency eigenvalue of G with multiplicity k≥1.A star complement H forμin G is an induced subgraph of G of order n-k with no eigenvalueμ,and the subset X=V(G-H)is called a st...Let G be a graph of order n andμbe an adjacency eigenvalue of G with multiplicity k≥1.A star complement H forμin G is an induced subgraph of G of order n-k with no eigenvalueμ,and the subset X=V(G-H)is called a star set forμin G.The star complement provides a strong link between graph structure and linear algebra.In this paper,the authors characterize the regular graphs with K2,2,s(s≥2)as a star complement for all possible eigenvalues,the maximal graphs with K2,2,s as a star complement for the eigenvalueμ=1,and propose some questions for further research.展开更多
文摘A function f: V( G)→{1,1} defined on the vertices of a graph G is a signed total dominating function (STDF) if the sum of its function values over any open neighborhood is at least one. An STDF f is minimal if there does not extst a STDF g: V(G)→{-1,1}, f≠g, for which g ( v )≤f( v ) for every v∈V( G ). The weight of a STDF is the sum of its function values over all vertices. The signed total domination number of G is the minimum weight of a STDF of G, while the upper signed domination number of G is the maximum weight of a minimal STDF of G, In this paper, we present sharp upper bounds on the upper signed total domination number of a nearly regular graph.
基金supported by the National Natural Science Foundation of China(Grant Nos.61502101 and 61170321)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20140651)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20110092110024)
文摘Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs(SRGs) with parameters(N, k, λ, μ) achieves full quantum speedup. The problem is reconsidered in terms of scattering quantum walk, a type of discrete-time quantum walks. Here, the search space is confined to a low-dimensional subspace corresponding to the collapsed graph of SRGs. To quantify the algorithm's performance, we leverage the fundamental pairing theorem, a general theory developed by Cottrell for quantum search of structural anomalies in star graphs.The search algorithm on the SRGs with k scales as N satisfies the theorem, and results can be immediately obtained, while search on the SRGs with k scales as√N does not satisfy the theorem, and matrix perturbation theory is used to provide an analysis. Both these cases can be solved in O(√N) time steps with a success probability close to 1. The analytical conclusions are verified by simulation results on two SRGs. These examples show that the formalism on star graphs can be applied more generally.
基金supported by National Natural Science Foundation of China(No.11571091)Natural Science Foundation of Hebei Province,China(No.F2019205147)Innovation Program of Hebei Normal University,China(No.CXZZSS2020050).
文摘A generalized strongly regular graphof grade p,as anew generalization of strongly regular graphs,is a regular graph such that the number of common neighbours of both any two adjacent vertices and any two non-adjacent vertices takes on p distinct values.For any vertex u of a generalized strongly regular graph of grade 2 with parameters(n,k;a_(1),a_(2);c_(1),c_(2)),if the number of the vertices that are adjacent to u and share ai(i=1,2)common neighbours with u,or are non-adjacent to u and share c,(i=1,2)common neighbours with is independent of the choice of the vertex u,then the generalized strongly regular graph of grade 2 is free.In this paper,we investigate the generalized strongly regular graph of grade 2 with parameters(n,k;k-1,a_(2);k-1,c_(2))and provide the sufficient and necessary conditions for the existence of a family of free generalized strongly regular graphs of grade 2.
基金supported by the National Natural Science Foundation of China(No.11571044)the Natural Science Foundation of Shanxi Province(No.201901D211106)。
文摘Fault diagnosis is an important area of study with regard to the design and maintenance of multiprocessor systems.A new measure for fault diagnosis of systems,namely,non-inclusive diagnosability(denoted by MM^(*)),was proposed by Ding et al.In this paper,we establish the non-inclusive diagnosability of a class of regular graphs under the PMC model and the MM^(*)model.As applications,the non-inclusive diagnosabilities of hypercubes,hierarchical hypercubes,folded hypercubes,star graphs,bubble-sort graphs,pancake graphs and dual cubes are determined under the PMC model and the[Math Processing Error]model.
文摘The goal of the present paper is to provide a gallery of small directed strongly regular graphs.For each graph of order n≤12 and valency k<n/2,a diagram is depicted,its relation to other small directed strongly regular graphs is revealed,the full group of automorphisms is described,and some other nice properties are given.To each graph a list of interesting subgraphs is provided as well.
基金supported by NNSF of China(No.11671376)the Fundamental Research Funds for the Central Universities.
文摘An(s,t)-partition of a graph G=(V,E)is a partition of V=V 1∪V 2 suchthatδ(G[V_(1)])≥s andδ(G[V_(2)])≥t.Ithasbeenconjecturedthat,forsufficiently large n,every d-regular graph of order n has a(d/2,d/2)-partition(called an internal partition).Inthispaper,weprovethateveryd-regulargraphofordern hasa(d/2,d/2)partition(called a weak internal partition)for d≤9 and sufficiently large n.
基金FRGHong Kong Baptist University NSFC (60673047)SRFDP (20040422004) of China
文摘Plesnik in 1972 proved that an (m - 1)-edge connected m-regular graph of even order has a 1-factor containing any given edge and has another 1-factor excluding any given m - 1 edges. Alder et al. in 1999 showed that if G is a regular (2n + 1)-edge-connected bipartite graph, then G has a 1-factor containing any given edge and excluding any given matching of size n. In this paper we obtain some sufficient conditions related to the edge-connectivity for an n-regular graph to have a k-factor containing a set of edges and (or) excluding a set of edges, where 1 ≤ k ≤n/2. In particular, we generalize Plesnik's result and the results obtained by Liu et al. in 1998, and improve Katerinis' result obtained 1993. Furthermore, we show that the results in this paper are the best possible.
基金Supported by Natural Sciences and Engineering Research Council of CanadaNNSF (Grant No. 10871119)RSDP (Grant No. 200804220001) of China
文摘For any even integer k and any integer i, we prove that a (kr +i)-regular multigraph contains a k-factor if it contains no more than kr - 3k/2+ i + 2 cut edges, and this result is the best possible to guarantee the existence of k-factor in terms of the number of cut edges. We further give a characterization for k-factor free regular graphs.
文摘A graph G is k-covered if each edge of G belongs to a k-factor of G. We determine some valuee of k for which every r-regular graph with edge-connectivity λ is k-covered.
基金Supported by Slovak VEGA Grant 1/0130/12Higher Education Commission Pakistan (Grant No.HEC(FD)/2007/555)the Ministry of Education of the Czech Republic (Grant No. MSM6198910027)
文摘Let G = (V, E) be a finite, simple and undirected graph with p vertices and q edges. An (a, d)-vertex-antimagic total labeling of G is a bijection f from V(G) t2 E(G) onto the set of consecutive integers 1, 2,... ,p + q, such that the vertex-weights form an arithmetic progression with the initial term a and difference d, where the vertex-weight of x is the sum of the value f(x) assigned to the vertex x together with all values f(xy) assigned to edges xy incident to x. Such labeling is called super if the smallest possible labels appear on the vertices. In this paper, we study the properties of such labelings and examine their existence for 2r-regular graphs when the difference d is 0, 1,..., r + 1.
基金Supported by the National Natural Science Foundation of China(No.61170302)Innovation Project of Optimization and Control of Network Systems of Zhejiang Normal University(ZSDZZZZXK03)
文摘Let Гt-(G) be upper minus total domination number of G. In this paper, We establish an upper bound of the upper minus total domination number of a regular graph G and characterize the extremal graphs attaining the bound. Thus, we answer an open problem by Yan, Yang and Shan
文摘The definition of the ascending subgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular graphs under some conditions do have an ascending subgraph decomposition.
基金supported by the European Regional Development Fund through the program COMPETEby the Portuguese Government through the FCT—Fundacao para a Ciencia e a Tecnologia under the project PEst—C/MAT/UI0144/2013+1 种基金partially supported by Portuguese Funds trough CIDMA—Center for Research and development in Mathematics and Applications,Department of Mathematics,University of Aveiro,3810-193,Aveiro,Portugalthe Portuguese Foundation for Science and Technology(FCT-Fundacao para a Ciencia e Tecnologia),within Project PEst-OE/MAT/UI4106/2014
文摘We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility conditions are deduced. Furthermore, we establish some relations between the classical Krein parameters and the generalized Krein parameters.
基金Supported by the Anhui Provincial Natural Science Foundation(050460102)National Natural Science Foundation of China(10601001,10571163)+3 种基金NSF of Department of Education of Anhui Province(2004kj027,2005kj005zd)Foundation of Anhui Institute of Architecture and Industry(200510307)Foundation of Mathematics Innovation Team of Anhui UniversityFoundation of Talents Group Construction of Anhui University
文摘In this paper, an equivalent condition of a graph G with t (2≤ t ≤n) distinct Laplacian eigenvalues is established. By applying this condition to t = 3, if G is regular (necessarily be strongly regular), an equivalent condition of G being Laplacian integral is given. Also for the case of t = 3, if G is non-regular, it is found that G has diameter 2 and girth at most 5 if G is not a tree. Graph G is characterized in the case of its being triangle-free, bipartite and pentagon-free. In both cases, G is Laplacian integral.
基金supported by the National Natural Science Foundation of China(No.51877013),(ZJ),(http://www.nsfc.gov.cn/)the Natural Science Foundation of Jiangsu Province(No.BK20181463),(ZJ),(http://kxjst.jiangsu.gov.cn/)sponsored by Qing Lan Project of Jiangsu Province(no specific grant number),(ZJ),(http://jyt.jiangsu.gov.cn/).
文摘Currently,functional connectomes constructed from neuroimaging data have emerged as a powerful tool in identifying brain disorders.If one brain disease just manifests as some cognitive dysfunction,it means that the disease may affect some local connectivity in the brain functional network.That is,there are functional abnormalities in the sub-network.Therefore,it is crucial to accurately identify them in pathological diagnosis.To solve these problems,we proposed a sub-network extraction method based on graph regularization nonnegative matrix factorization(GNMF).The dynamic functional networks of normal subjects and early mild cognitive impairment(eMCI)subjects were vectorized and the functional connection vectors(FCV)were assembled to aggregation matrices.Then GNMF was applied to factorize the aggregation matrix to get the base matrix,in which the column vectors were restored to a common sub-network and a distinctive sub-network,and visualization and statistical analysis were conducted on the two sub-networks,respectively.Experimental results demonstrated that,compared with other matrix factorization methods,the proposed method can more obviously reflect the similarity between the common subnetwork of eMCI subjects and normal subjects,as well as the difference between the distinctive sub-network of eMCI subjects and normal subjects,Therefore,the high-dimensional features in brain functional networks can be best represented locally in the lowdimensional space,which provides a new idea for studying brain functional connectomes.
基金National Natural Science Foundations of China(Nos.61362001,61102043,61262084)Technology Foundations of Department of Education of Jiangxi Province,China(Nos.GJJ12006,GJJ14196)Natural Science Foundations of Jiangxi Province,China(Nos.20132BAB211030,20122BAB211015)
文摘The imaging speed is a bottleneck for magnetic resonance imaging( MRI) since it appears. To alleviate this difficulty,a novel graph regularized sparse coding method for highly undersampled MRI reconstruction( GSCMRI) was proposed. The graph regularized sparse coding showed the potential in maintaining the geometrical information of the data. In this study, it was incorporated with two-level Bregman iterative procedure that updated the data term in outer-level and learned dictionary in innerlevel. Moreover,the graph regularized sparse coding and simple dictionary updating stages derived by the inner minimization made the proposed algorithm converge in few iterations, meanwhile achieving superior reconstruction performance. Extensive experimental results have demonstrated GSCMRI can consistently recover both real-valued MR images and complex-valued MR data efficiently,and outperform the current state-of-the-art approaches in terms of higher PSNR and lower HFEN values.
基金supported by the fund of South China Agricultural University (4900-K08225)supported by the National Natural Science Foundation of China(10771080)Specialized Research Fund for the Doctoral Program of Higher Eduction (20070574006)
文摘A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant A such that the equality λd(ui) = ∑(vi,vj)∈E(G) d(vj) holds for all i = 1, 2,…, |V(G)|, where d(vi) denotes the degree of vertex vi. In this paper, some harmonic properties of the complement and line graph are given, and some algebraic properties for the λ-Hgraphs are obtained.
基金National Natural Science Foundation of China(No.11371086)the Fund of Science and Technology Commission of Shanghai Municipality,China(No.13ZR1400100)
文摘Let LE(G) denote the Laplacian energy of a graph G. In this paper the xyz-transformations G^(xyz) of an r-regular graph G for x,y,z∈{0,1, +,-} are considered. The explicit formulas of LE(G^(xyz)) are presented in terms of r,the number of vertices of G for any positive integer r and x,y,z∈{ 0,1},and also for r = 2 and all x,y,z∈{0,1,+,-}. Some Laplacian equienergetic pairs of G^(xyz) for r = 2 and x,y,z∈{0,1, +,-} are obtained. This also provides several ways to construct infinitely many pairs of Laplacian equienergetic graphs.
基金supported by the Teaching Reform Research Project of Qinghai Minzu University,China(2021-JYYB-009)the“Chunhui Plan”Cooperative Scientific Research Project of the Ministry of Education of China(2018).
文摘Link prediction has attracted wide attention among interdisciplinaryresearchers as an important issue in complex network. It aims to predict the missing links in current networks and new links that will appear in future networks.Despite the presence of missing links in the target network of link prediction studies, the network it processes remains macroscopically as a large connectedgraph. However, the complexity of the real world makes the complex networksabstracted from real systems often contain many isolated nodes. This phenomenon leads to existing link prediction methods not to efficiently implement the prediction of missing edges on isolated nodes. Therefore, the cold-start linkprediction is favored as one of the most valuable subproblems of traditional linkprediction. However, due to the loss of many links in the observation network, thetopological information available for completing the link prediction task is extremely scarce. This presents a severe challenge for the study of cold-start link prediction. Therefore, how to mine and fuse more available non-topologicalinformation from observed network becomes the key point to solve the problemof cold-start link prediction. In this paper, we propose a framework for solving thecold-start link prediction problem, a joint-weighted symmetric nonnegative matrixfactorization model fusing graph regularization information, based on low-rankapproximation algorithms in the field of machine learning. First, the nonlinear features in high-dimensional space of node attributes are captured by the designedgraph regularization term. Second, using a weighted matrix, we associate the attribute similarity and first order structure information of nodes and constrain eachother. Finally, a unified framework for implementing cold-start link prediction isconstructed by using a symmetric nonnegative matrix factorization model to integrate the multiple information extracted together. Extensive experimental validationon five real networks with attributes shows that the proposed model has very goodpredictive performance when predicting missing edges of isolated nodes.
基金supported by the National Natural Science Foundation of China(No.11971180,12271337)the Guangdong Provincial Natural Science Foundation(No.2019A1515012052)。
文摘Let G be a graph of order n andμbe an adjacency eigenvalue of G with multiplicity k≥1.A star complement H forμin G is an induced subgraph of G of order n-k with no eigenvalueμ,and the subset X=V(G-H)is called a star set forμin G.The star complement provides a strong link between graph structure and linear algebra.In this paper,the authors characterize the regular graphs with K2,2,s(s≥2)as a star complement for all possible eigenvalues,the maximal graphs with K2,2,s as a star complement for the eigenvalueμ=1,and propose some questions for further research.