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有向图和二部有向图的局部边连通性 被引量：2

LOCAL -EDGE- CONNECTIVITY OF DIGRAPHS AND BIPARTITE DIGRAPHS
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摘要 笔者首先利用顶点的度和给出了有向图是超级局部边连通的一个最好可能的充分条件,然后提出了二部有向图为极大局部边连通和超级局部边连通的度序列条件.这些结果在网络可靠性分析中有一定应用. This paper presents a best possible sufficient condition in term of degree sum for a digraph to be super- local -edge -connected. Using degree sequence we give sufficient conditions for a bipartite digraph to be maximally local -edge -connected and super -local -edge -connected. These results have applications in analy- sis of network reliability.
作者 高敬振 吴芳
机构地区 山东师范大学数学科学学院
出处 《山东师范大学学报（自然科学版）》 CAS 2012年第1期20-24,31,共6页 Journal of Shandong Normal University(Natural Science)
基金 国家自然科学基金资助项目（10901097） 山东省自然科学基金资助项目（ZR2010AQ003） 山东省高等学校科技计划项目（J10LA11）.
关键词 有向图 二部有向图 极大局部边连通性 超级局部边连通性 digraph bipartite digraph maximal - local - edge - connectivity super - local - edge - connectivity
分类号 O157.5 [理学—基础数学]
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参考文献10

  • 1Bollobas B. Modern Graph Theory [ M ]. New York : Springer - Verlag, 1998.
  • 2王世英,林上为.网络边连通性的最优化[M].北京:科学出版社,2009.
  • 3Hellwig A, Volkmann L. Maximally edge -connected and vertex -connected graphs and digraphs: A survey[J]. Discrete Math ,2008,308:3265 - 3296.
  • 4Hellwig A, Volkmann L. Maximally local -edge -connected graphs and digraphs [ J]. Ars Combin,2004,72:295 -306.
  • 5Fiol M A. On super- edge- connected digraphs and bipartite digraphs [ J]. J Graph Theory, 1992,16:545 -555.
  • 6Dankelmann P, Volkmann L. Degree sequence conditions for maximally edge -connected graphs and digraphs[ J ]. J Graph Theory, 1997,26:27 - 34.
  • 7Volkmann L. Degree sequence conditions for super - edge - connected graphs and digraphs[J]. Ars Combin, 2003, 67 : 237 -249.
  • 8Hellwig A, Volkmann L. Maximally edge- connected digraphs[ J ]. Australas J C ombin ,2003,27:23 -32.
  • 9Volkmann L. Local- edge- connectivity in digraphs and oriented graphs[J]. Discrete Math, 2007, 307:3207 -3212.
  • 10Volkmann L. On local connectivity of graphs with given clique number[ J ]. J Graph Theory, 2010, 63 : 192 - 197.

共引文献5

同被引文献12

  • 1HELLWIG A, VOLKMANN L. Maximally edge-connected and vertex-connected graphs and diagraphs: a survey [ J ]. Discrete Math, 2008, 308( 15): 3265-3296.
  • 2BAUER D, BOESCH F, SUFFEL C, et al. Connectivity extremal problems and the design of reliable probabilistic networks [ C ]// The Theory and Application of Graphs:Proceedings of the 4th international conference on the theory and applications of graphs. New York: John Wiley & Sons, Inc, 1981:45 -54.
  • 3HELLWIG A, VOLKMANN L. Maximally local-edge-connected graphs and digraphs [ J]. Ars Combin, 2004, 72:295 -306.
  • 4HELLWIG A, VOLKMANN L. Neighborhood conditions for graphs and digraphs to be maximally edge-connected[ J]. Australas J Combin, 2005, 33:265-277.
  • 5HELLWIG A, VOLKMANN L. Neighborhood and degree conditions for super-edge-connected bipartite digraphs [ J ]. Result Math, 2004, 45:45 -58.
  • 6HELLWIG A,VOLKMANN L. Maximally edge-connected and vertex-connected graphs and digraphs:A survey[J].Discrete Mathematics,2008,(15):3265-3296.doi:10.1016/j.disc.2007.06.035.
  • 7BAUER D,SUFFEL C,BOESCH F. Connectivity extremal problems and the design of reliable probabilistic networks[M].The Theory and Application of Graphs.New York:John Wiley & Sons,1981.45-54.
  • 8HELLWIG A,VOLKMANN L. Maximally local-edge-connected graphs and digraphs[J].ARS Combinatoria,2004.295-306.
  • 9HELLWIG A,VOLKMANN L. Maximally edge-connected digraphs[J].Australasian Journal of Combinatorics,2003.23-32.
  • 10HELLWIG A,VOLKMANN L. Neighborhood and degree conditions for super-edge-connected bipartite digraphs[J].Results in Mathematics,2004,(1-2):45-58.

引证文献2

二级引证文献1

山东师范大学学报（自然科学版）
2012年 第1期

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