计算机工程与应用 ›› 2013, Vol. 49 ›› Issue (22): 1-2.

• 博士论坛 • 上一篇    下一篇

给定匹配数的单圈图的最小值

张惠玲1,2,曲安京2   

  1. 1.西安航空学院 理学院,西安 710077
    2.西北大学 数学系,西安 710127
  • 出版日期:2013-11-15 发布日期:2013-11-15

Unicyclic graphs with given matching number that have minmum general Randic index

ZHANG Huiling1,2, QU Anjing2   

  1. 1.School of Science, Xi’an Aerotechnical University, Xi’an 710077, China
    2.Department of Mathematics, Northwestern University, Xi’an 710127, China
  • Online:2013-11-15 Published:2013-11-15

摘要: 图[G]的广义Randic指标定义为[Rα(G)=uv∈E(G)(dudv)α],其中[α]为任意实数,[du]为顶点[u]的度。顶点数等于边数的简单图称为单圈图。在匹配数等于边数的情况下,通过分类讨论,给出当[-1.39α-1]时,相应单圈图的广义Randic指标的最小值,并给出相应的结构图。

关键词: 单圈图, 匹配, 广义Randic指标

Abstract: The general Randic index [Rα(G)] is the sum of the weights [(dudv)α] over all edges [uv] of a graph [G], where [α] is a real number and [du] is the degree of the vertex [u] of [G]. In this paper, for[-1.39α-1], the minimum general Randic index [Rα(G)] among all the conjugated unicyclic graphs is determined and the corresponding extremal conjugated uinicyclic graphs are characterized.

Key words: uinicyclic graphs, matching, the general Randic index