On the maximal eccentric connectivity indices of graphs

作     者：ZHANG Jian-bin LIU Zhong-zhu ZHOU Bo 

作者机构：School of Mathematics South China Normal University Department of Mathematics Huizhou University 

出 版 物：《Applied Mathematics(A Journal of Chinese Universities)》 (高校应用数学学报（英文版）（B辑）)

年 卷 期：2014年第29卷第3期

页      面：374-378,F0003页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by China Postdoctoral Science Foundation(2012M520815 and 2013T60411) the National Natural Science Foundation of China(11001089) 

主　　题：Eccentric connectivity index diameter distance 

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 ∑vЕV（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 and m edges （m ≥ n ＋ 5）. among the connected graphs with n vertices