A POLYNOMIAL ALGORITHM FOR FINDING THEMINIMUM FEEDBACK VERTEX SET OF A3-REGULAR SIMPLE GRAPH

A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided.

The Spectral Radii of Some Adhesive Graphs

The spectral radius of a graph is the maximum eigenvalues of its adjacency matrix. In this paper, using the property of quotient graph, the sharp upper bounds for the spectral radii of some adhesive graphs are determined.

On the Number of Cycles in a Graph

In this paper, we obtain explicit formulae for the number of 7-cycles and the total number of cycles of lengths 6 and 7 which contain a specific vertex vi in a simple graph G, in terms of the adjacency matrix and with the help of combinatorics.

On the Non-Common Neighbourhood Energy of Graphs

In this paper, we introduce a new type of graph energy called the non-common-neighborhood energy ,?,?NCN-energy for some standard graphs is obtained and an upper bound for ?is found when G is a strongly regular graph. Also the relation between common neigh-bourhood energy and non-common neighbourhood energy of a graph is established.

Structural Synthesis of Compliant Metamorphic Mechanisms Based on Adjacency Matrix Operations

A compliant metamorphic mechanism attributes to a new type of metamorphic mechanisms evolved from rigid metamorphic mechanisms. The structural characteristics and representations of a compliant metamorphic mechanism are different from its rigid counterparts, so does the structural synthesis method. In order to carry out its structural synthesis, a constraint graph representation for topological structure of compliant metamorphic mechanisms is introduced, which can not only represent the structure of a compliant metamorphic mechanism, but also describe the characteristics of its links and kinematic pairs. An adjacency matrix representation of the link relationships in a compliant metamorphic mechanism is presented according to the constraint graph. Then, a method for structural synthesis of compliant metamorphic mechanisms is proposed based on the adjacency matrix operations. The operation rules and the operation procedures of adjacency matrices are described through synthesis of the initial configurations composed of s＋1 links from an s-link mechanism （the final configuration）. The method is demonstrated by synthesizing all the possible four-link compliant metamorphic mechanisms that can transform into a three-link mechanism through combining two of its links. Sixty-five adjacency matrices are obtained in the synthesis, each of which corresponds to a compliant metamorphic mechanism having four links. Therefore, the effectiveness of the method is validated by a specific compliant metamorphic mechanism corresponding to one of the sixty-five adjacency matrices. The structural synthesis method is put into practice as a fully compliant metamorphic hand is presented based on the synthesis results. The synthesis method has the advantages of simple operation rules, clear geometric meanings, ease of programming with matrix operation, and provides an effective method for structural synthesis of compliant metamorphic mechanisms and can be used in the design of new compliant metamorphic mechanisms.

Privacy-Preserving Multi-Keyword Fuzzy Adjacency Search Strategy for Encrypted Graph in Cloud Environment

In a cloud environment,outsourced graph data is widely used in companies,enterprises,medical institutions,and so on.Data owners and users can save costs and improve efficiency by storing large amounts of graph data on cloud servers.Servers on cloud platforms usually have some subjective or objective attacks,which make the outsourced graph data in an insecure state.The issue of privacy data protection has become an important obstacle to data sharing and usage.How to query outsourcing graph data safely and effectively has become the focus of research.Adjacency query is a basic and frequently used operation in graph,and it will effectively promote the query range and query ability if multi-keyword fuzzy search can be supported at the same time.This work proposes to protect the privacy information of outsourcing graph data by encryption,mainly studies the problem of multi-keyword fuzzy adjacency query,and puts forward a solution.In our scheme,we use the Bloom filter and encryption mechanism to build a secure index and query token,and adjacency queries are implemented through indexes and query tokens on the cloud server.Our proposed scheme is proved by formal analysis,and the performance and effectiveness of the scheme are illustrated by experimental analysis.The research results of this work will provide solid theoretical and technical support for the further popularization and application of encrypted graph data processing technology.

Adjacent Vertex Distinguishing I-total Coloring of Outerplanar Graphs

Let G be a simple graph with no isolated edge. An/-total coloring of a graphG is a mapping Ф ： V（G） U E（G） → （1, 2,…… , k） such that no adjacent vertices receive thesame color and no adjacent edges receive the same color. An/-total coloring of a graph G issaid to be adjacent vertex distinguishing if for any pair of adjacent vertices u and v of G, wehave CФ（u） ≠ CФ（v）, where CФ（u） denotes the set of colors of u and its incident edges. Theminimum number of colors required for an adjacent vertex distinguishing I-total coloring of GG is called the adjacent vertex distinguishing I-total chromatic number, denoted by Xat（G）.In this paper, we characterize the adjacent vertex distinguishing I-total chromatic numberof outerplanar graphs.

Aunu Integer Sequence as Non-Associative Structure and Their Graph Theoretic Properties

The generating function for generating integer sequence of Aunu numbers of prime cardinality was reported earlier by the author in [1]. This paper assigns an operator on the function for where the operation induces addition or subtraction on the pairs of ai, aj elements which are consecutive pairs of elements obtained from a generating set of some finite order. The paper identifies that the set of the generated pairs of integer sequence is non-associative. The paper also presents the graph theoretic applications of the integers generated in which subgraphs are deduced from the main graph and adjacency matrices and incidence matrices constructed. It was also established that some of the subgraphs were found to be regular graphs. The findings in this paper can further be used in coding theory, Boolean algebra and circuit designs.

Adjacent Vertex-distinguishing E-total Coloring on Some Join Graphs Cm ∨ Gn

Let G(V, E) be a simple connected graph and k be positive integers. A mapping f from V∪E to {1, 2, ··· , k} is called an adjacent vertex-distinguishing E-total coloring of G(abbreviated to k-AVDETC), if for uv ∈ E(G), we have f(u) ≠ f(v), f(u) ≠ f(uv), f(v) ≠ f(uv), C(u) ≠C(v), where C(u) = {f(u)}∪{f(uv)|uv ∈ E(G)}. The least number of k colors required for which G admits a k-coloring is called the adjacent vertex-distinguishing E-total chromatic number of G is denoted by x^e_(at) (G). In this paper, the adjacent vertexdistinguishing E-total colorings of some join graphs C_m∨G_n are obtained, where G_n is one of a star S_n , a fan F_n , a wheel W_n and a complete graph K_n . As a consequence, the adjacent vertex-distinguishing E-total chromatic numbers of C_m∨G_n are confirmed.

Block Matrix Representation of a Graph Manifold Linking Matrix Using Continued Fractions

We consider the block matrices and 3-dimensional graph manifolds associated with a special type of tree graphs. We demonstrate that the linking matrices of these graph manifolds coincide with the reduced matrices obtained from the Laplacian block matrices by means of Gauss partial diagonalization procedure described explicitly by W. Neumann. The linking matrix is an important topological invariant of a graph manifold which is possible to interpret as a matrix of coupling constants of gauge interaction in Kaluza-Klein approach, where 3-dimensional graph manifold plays the role of internal space in topological 7-dimensional BF theory. The Gauss-Neumann method gives us a simple algorithm to calculate the linking matrices of graph manifolds and thus the coupling constants matrices.

Smarandachely Adjacent-vertex-distinguishing Proper Edge Coloring ofK4 ∨ Kn

Let f be a proper edge coloring of G using k colors.For each x∈V(G),the set of the colors appearing on the edges incident with x is denoted by S_f(x)or simply S(x)if no confusion arise.If S(u)■S(v)and S(v)■S(u)for any two adjacent vertices u and v,then f is called a Smarandachely adjacent vertex distinguishing proper edge coloring using k colors,or k-SA-edge coloring.The minimum number k for which G has a Smarandachely adjacent-vertex-distinguishing proper edge coloring using k colors is called the Smarandachely adjacent-vertex-distinguishing proper edge chromatic number,or SAedge chromatic number for short,and denoted byχ'_(sa)(G).In this paper,we have discussed the SA-edge chromatic number of K_4∨K_n.

IMPROVEMENT AND REALIZATION FOR THE MAXIMUM WEIGHT MATCHING ALGORITHM

Some new concepts of effective incidence matrix,ascending order adjacency matrix andend-result vertex are introduced,and some improvements of the maximum weight matchingalgorithm are made.With this method a computer program in FORTRAN language is realized onthe computers FELIX C-512 and IBM-PC.Good results are obtained in practical operations.

Introducing Weighted Nodes to Evaluate the Cloud Computing Topology

Typical data centers house several powerful ICT (Information and Communication Technology) equipment such as servers, storage devices and network equipment that are high-energy consuming. The nature of these high-energy consuming equipment is mostly accountable for the very large quantities of emissions which are harmful and unfriendly to the environment. The costs associated with energy consumption in data centers increases as the need for more computational resources increases, so also the appalling effect of CO2 (Carbon IV Oxide) emissions on the environment from the constituent ICT facilities-Servers, Cooling systems, Telecommunication systems, Printers, Local Area Network etc. Energy related costs would traditionally account for about 42% (forty-two per cent) of the total costs of running a typical data center. There is a need to have a good balance between optimization of energy budgets in any data center and fulfillment of the Service Level Agreements (SLAs), as this ensures continuity/profitability of business and customer’s satisfaction. A greener computing from what used to be would not only save/sustain the environment but would also optimize energy and by implication saves costs. This paper addresses the challenges of sustainable (or green computing) in the cloud and proffer appropriate, plausible and possible solutions. The idle and uptime of a node and the traffic on its links (edges) has been a concern for the cloud operators because as the strength and weights of the links to the nodes (data centres) increases more energy are also being consumed by and large. It is hereby proposed that the knowledge of centrality can achieve the aim of energy sustainability and efficiency therefore enabling efficient allocation of energy resources to the right path. Mixed-Mean centrality as a new measure of the importance of a node in a graph is introduced, based on the generalized degree centrality. The mixed-mean centrality reflects not only the strengths (weights) and numbers of edges for degree centrality but it combines these features by also applying the closeness centrality measures while it goes further to include the weights of the nodes in the consideration for centrality measures. We illustrate the benefits of this new measure by applying it to cloud computing, which is typically a complex system. Network structure analysis is important in characterizing such complex systems.

Adjacent Vertex Distinguishing Total Coloring of M（Tn）

如果为任何东西二个邻近的顶点有不同颜色 sets.According 到树的性质， G 的 k 合适的全部的着色被称为邻近的区分，区分全部的色彩的数字的邻近的顶点将用方法为树的 Mycielski 图被决定感应。

The Adjacency Codes of the First Yellow Graphs

The authors study the binary codes spanned by the adjacency matrices of the strongly regular graphs(SRGs)on at most two hundred vertices whose existence is unknown.The authors show that in length less than one hundred they cannot be cyclic,except for the exceptions of the SRGs of parameters(85,42,20,21)and(96,60,38,36).In particular,the adjacency code of a(85,42,20,21)is the zero-sum code.In the range[100,200]the authors find 29 SRGs that could possibly have a cyclic adjacency code.

An Intelligent Identification Approach of Assembly Interface for CAD Models

Kinematic semantics is often an important content of a CAD model(it refers to a single part/solid model in this work)in many applications,but it is usually not the belonging of the model,especially for the one retrieved from a common database.Especially,the effective and automatic method to reconstruct the above information for a CAD model is still rare.To address this issue,this paper proposes a smart approach to identify each assembly interface on every CAD model since the assembly interface is the fundamental but key element of reconstructing kinematic semantics.First,as the geometry of an assembly interface is formed by one or more adjacent faces on each model,a face-attributed adjacency graph integrated with face structure fingerprint is proposed.This can describe each CAD model as well as its assembly interfaces uniformly.After that,aided by the above descriptor,an improved graph attention network is developed based on a new dual-level anti-interference filtering mechanism,which makes it have the great potential to identify all representative kinds of assembly interface faces with high accuracy that have various geometric shapes but consistent kinematic semantics.Moreover,based on the abovementioned graph and face-adjacent relationships,each assembly interface on a model can be identified.Finally,experiments on representative CAD models are implemented to verify the effectiveness and characteristics of the proposed approach.The results show that the average assembly-interface-face-identification accuracy of the proposed approach can reach 91.75%,which is about 2%–5%higher than those of the recent-representative graph neural networks.Besides,compared with the state-of-the-art methods,our approach is more suitable to identify the assembly interfaces(with various shapes)for each individual CAD model that has typical kinematic pairs.

基于图神经网络的零件机加工特征识别方法

针对现有基于深度学习的方法存在的难以识别相交特征、无法精确确定加工特征面的问题,提出基于图神经网络的加工特征识别方法.通过压缩激励模块提取节点与邻接边的特征,构建节点级与邻接边级的双层注意力网络,分割每个节点对应的加工特征.该方法充分利用了零件模型的面特征与边特征,结合零件模型的拓扑结构,基于注意力机制对特征信息进行深度学习,可以有效地解决非面合并相交特征的识别问题.在多加工特征零件数据集上,将该方法与其他3种特征识别方法进行实验对比,在准确率、平均类准确率和交并比3项指标上均取得最优结果,识别准确率高于95%.

广义θ-图和广义梅花图φ的奇异性

利用奇异图的邻接矩阵行列式等于零的方法讨论广义θ-图和广义梅花图φ的奇异性,分别给出广义θ-图θ(a_(1),a_(2),…,a_(k))和广义梅花图φ(a_(1),a_(2),…,a_(k))是奇异图的充分必要条件,并计算这两类图中奇异图发生的概率值.