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具有最小Wiener指数的双圈图 被引量：3

Bicyclic Graphs with Minimum Wiener Index
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摘要 一个图G的Wiener指数W(G)定义为G中所有点对的距离和,双圈图是一个具有n个点和n+1条边的连通图,我们根据两个圈的相对位置关系把双圈图分成三类,分别在这三类中给出了最小的Wiener指数,然后通过比较三类极值的大小得到了双圈图中具有最小Wiener指数的图。 The Wiener index W（G） of a graph G is defined as the sum of distances over all pairs of vertices. Bicyclic graphis a connected simple graph n with n ＋ 1 vertices and edges. According to the locational relation of the two cycles, we divide bicyelie graphs into three subsets, and their bicyclic graphs with minimum Wiener index in this subsets are given, respectively. By comparing the Wiener index of graphs with extremal value in those sets, we obtain bicyclic grahs with minimum Wiener index.
作者 邵云 邢抱花 杨光
机构地区 安徽大学数学科学学院 安庆师范学院数学与计算科学学院
出处 《安庆师范学院学报（自然科学版）》 2009年第3期8-12,共5页 Journal of Anqing Teachers College(Natural Science Edition)
关键词 双圈图 WIENER指数 最小 bicydic graph, wiener index, minimum
分类号 O157 [理学—基础数学]
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参考文献11

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同被引文献18

  • 1Dobryin A A, Entringer R, Gutman I. Wiener index of trees : Theory and Application [ J ]. Acta Appl Math,2001,66 : 211 - 249.
  • 2Bondy A, Mmurty U S R. Graph Theory with Applications [ M ]. New York:Macmillan Press, 1976.
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  • 4H. D. Liu and M. Lu. A unified approach to extremal cacti for different indices[J]. Match Commun. Math. Comput. Chem. ,2007,58( 1 ) :183 - 194.
  • 5H. D. Liu and X. F. Pan. On the Wiener index of Trees with Fixed Diameter [ J ]. Match Commun. Math. Comput. Chem. ,2008,60 ( 1 ) :85 - 94.
  • 6Bondy A, Mmurty U S R. Graph Theory with Application [ M ]. New York: Macmillan Press, 1976.
  • 7Dobryin A A, Entringer R, Gutman I. Wiener index of trees: Theory and Application[J]. Acta Appl Math,2001 (66) :211 - 249.
  • 8K. Xu, K. C. Das. Extremal Unieyelie and Bieyelie Graphs with Respect to Harary Index [ J ]. Bull. Malays. Math. Sei. Soe ( 2 ), 2013,36(2) :373 -383.
  • 9K. Xu, N. Trinajstie. Hyper - Wiener and Harary indices of graphs with cut edges[J]. Util. Math. ,2011 (84) :153 -163.
  • 10G. Yu, L. Feng. On the maximal Harary index of a class of bi- eyelie graphs[J]. Util. Math. ,2010 (82) : 285 - 292.

引证文献3

安庆师范学院学报（自然科学版）
2009年 第3期

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