On the maximal eccentric connectivity indices of graphs

被引：0

作者：

ZHANG Jian-bin ^{[1
]}

LIU Zhong-zhu ^{[2
]}

ZHOU Bo ^{[1
]}

机构：

[1] School of Mathematics, South China Normal University

[2] Department of Mathematics, Huizhou University

来源：

Applied Mathematics:A Journal of Chinese Universities | 2014年 / 03期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Eccentric connectivity index; diameter; distance;

D O I：

暂无

中图分类号：

O157.5 [图论];

学科分类号：

070104 ;

摘要：

For a connected simple graph G, the eccentricity ec(v) of a vertex v in G is the distance from v to a vertex farthest from v, and d(v) denotes the degree of a vertex v. The eccentric connectivity index of G, denoted by ξc(G), is defined as v∈V(G)d(v)ec(v). In this paper, we will determine the graphs with maximal eccentric connectivity index among the connected graphs with n vertices and m edges(n ≤ m ≤ n + 4), and propose a conjecture on the graphs with maximal eccentric connectivity index among the connected graphs with n vertices and m edges(m ≥ n + 5).

引用

页码：374 / 378

页数：5