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The hamiltonicity on the competition graphs of round digraphs

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Applied Mathematics(A Journal of Chinese Universities) 2018年第4期33卷 409-420页

作者： ZHANG Xin-hong LI Rui-juan AN Xiao-ting Department of Applied Mathematics Taiyuan University of Science and Technology School of Mathematical Sciences Shanxi University

Given a digraph D =（V, A）, the competition graph G of D, denoted by C（D）, has the same set of vertices as D and an edge between vertices x and y if and only if N;（x）∩N;（y）≠Ф. In this paper, we investigate the competition graphs of round digraphs and give a necessary and sufficient condition for these graphs to be hamiltonian.

关键词： round digraph competition graph connected component hamiltonian

Commutative Rings Whose Zero-divisor Graph Is a Proper Refinement of a Star Graph

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Acta Mathematica Sinica,English Series 2011年第6期27卷 1221-1232页

作者： Qiong LIU Tong Suo WU Department of Mathematics and Physics Shanghai University of Electric Power Shanghai 201300 P. R. China Department of Mathematics Shanghai Jiaotong University Shanghai 200240 P. R. China

A graph is called a proper refinement of a star graph if it is a refinement of a star graph, but it is neither a star graph nor a complete graph. For a refinement of a star graph G with center c, let G＊ be the subgraph of G induced on the vertex set V（G）／ {c or end vertices adjacent to c}. In this paper, we study the isomorphic classification of some finite commutative local rings R by investigating their zero-divisor graphs G=Г（R）, which is a proper refinement of a star graph with exactly one center c. We determine all finite commutative local rings R such that G＊ has at least two connected components. We prove that the diameter of the induced graph G＊ is two if Z（R）2 ≠connected component, Z（R）3 = connected component and Gc is connected. We determine the structure of R which has two distinct nonadjacent vertices a, fl C Z（R）＊／{c} such that the ideal [N（a）N（β）]connected component is generated by only one element of Z（R）＊／{c}. We also completely determine the correspondence between commutative rings and finite complete graphs Kn with some end vertices adjacent to a single vertex of Kn.

关键词： Commutative rings zero-divisor graph minimal generating set connected component

Dual-stage constructed random graph algorithm to generate random graphs featuring the same topological characteristics with power grids

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Journal of Modern Power Systems and Clean Energy 2017年第5期5卷 683-695页

作者： Shiqian MA Yixin YU Lei ZHAO State Grid Tianjin Electric Power Research Institute Tianjin 300384China Key Laboratory of Smart Grid of Ministry of Education Tianjin UniversityTianjin 300072China

It is a common practice to simulate some historical or test systems to validate the efficiency of new methods or concepts. However, there are only a small number of existing power system test cases, and validation and evaluation results, obtained using such a limited number of test cases, may not be deemed sufficient or convincing. In order to provide more available test cases, a new random graph generation algorithm, named ‘‘dualstage constructed random graph’’ algorithm, is proposed to effectively model the power grid topology. The algorithm generates a spanning tree to guarantee the connectivity of random graphs and is capable of controlling the number of lines precisely. No matter how much the average degree is,whether sparse or not, random graphs can be quickly formed to satisfy the requirements. An approach is developed to generate random graphs with prescribed numbers of connected components, in order to simulate the power grid topology under fault conditions. Our experimental study on several realistic power grid topologies proves that the proposed algorithm can quickly generate a large number of random graphs with the topology characteristics of real-world power grid.

关键词： Power gird topology Dual-stage constructed random graph(DSCRG)algorithm Random graph generation Connectivity Average degree connected component

On Commuting Graph of Group Ring Z_nS_3

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Communications in Mathematical Research 2012年第4期28卷 313-323页

作者： GAO YAN-YAN TANG GAO-HUA CHEN JIAN-LONG Department of Mathematics Southeast University Nanjing 210096 School of Mathematical Sciences Guangxi Education University Nanning 530001

The commuting graph of an arbitrary ring R, denoted by Г（R）, is a graph whose vertices are all non-central elements of R, and two distinct vertices a and b are adjacent if and only if ab = ba. In this paper, we investigate the connectivity and the diameter of Г（ZnS3）. We show that Г（ZnS3） is connected if and only if n is not a prime number. If Г（ZnS3） is connected then diam（Г（ZnS3）） = 3, while ifГ（ZnS3） is disconnected then every connected component of Г（ZnS3） must be a complete graph with same size, and we completely determine the vertice set of every connected component.

关键词： group ring commuting graph connected component diameter of agraph

A Run-based Algorithm for Identifying connected components in Binary Images

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A Run-based Algorithm for Identifying Connected Components i...