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运筹学学报 ›› 2015, Vol. 19 ›› Issue (2): 45-53.doi: 10.15960/j.cnki.issn.1007-6093.2015.02.005

• 运筹学 • 上一篇    下一篇

三圈图的Harary指数

蔡改香1,*, 邢抱花1, 余桂东1   

  1. 1. 安庆师范学院数学与计算科学学院, 安徽安庆 246133
  • 收稿日期:2014-06-23 出版日期:2015-06-15 发布日期:2015-06-15
  • 通讯作者: 蔡改香 caigaixiang@qq.com
  • 基金资助:

    安徽省自然科学基金(No. 11040606M14), 安徽省高校自然科学基金(Nos. KJ2011A195, KJ2013A196), 安庆师范学院青年科学基金(No. KJ201307)

The Harary index of tricyclic graphs

CAI Gaixiang1,*, XING Baohua1, YU Guidong1   

  1. 1. School of Mathematics and Computation Sciences, Anqing Normal University, Anqing 246133, Anhui, China
  • Received:2014-06-23 Online:2015-06-15 Published:2015-06-15

PDF

1386

被引次数

3

摘要：

图G的Harary指数是指图G中所有顶点对间的距离倒数之和. 三圈图是指边数等于顶点数加2的连通图. 研究了三圈图的Harary数, 给出了所有三圈图中具有极大Harary指数的图的结构以及含有三个圈的三圈图中具有次大Harary指数的图的结构.

关键词: Harary 指数, 三圈图, 距离

Abstract:

The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a  graph. Tricyclic graphs are  connected graphs in which the number of edges equals the number of vertices plus two. In this paper, we determine graphs with the largest Harary index among all the tricyclic graphs, and we also give graphs with the second largest Harary index among all the tricyclic graphs with three cycles.

Key words: Harary index, tricyclic graph, distance