On the edge-Szeged index of unicyclic graphs with given diameter

被引：7

作者：

Wang, Guangfu ^{[1
]}

Li, Shuchao ^{[2
]}

Qi, Dongchao ^{[2
]}

Zhang, Huihui ^{[3
]}

机构：

[1] East China Jiaotong Univ, Sch Sci, Nanchang 330013, Jiangxi, Peoples R China

[2] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Hubei, Peoples R China

[3] Luoyang Normal Univ, Dept Math, Luoyang 471002, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 336卷

基金：

中国国家自然科学基金;

关键词：

Edge-Szeged index; Unicyclic graphs; Diameter; WIENER INDEX; TOPOLOGICAL INDEX; BIPARTITE GRAPHS; EXTREMAL CACTI; CONJECTURES; DISTANCE; RESPECT;

D O I：

10.1016/j.amc.2018.04.077

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a connected graph G, the edge Szeged index Sz(e)(G) is defined as Sz(e)(G) = Sigma e-uv is an element of E m(u)(e)m(v)(e), where m(u)(e) and m(v)(e) are, respectively, the number of edges of G lying closer to vertex u than to vertex v and the number of edges of G lying closer to vertex v than to vertex u. In this paper, some extremal problems on the edge-Szeged index of unicyclic graphs are considered. All the n-vertex unicyclic graphs with a given diameter having the minimum edge-Szeged index are identified. Using a unified approach we identify the n-vertex unicyclic graphs with the minimum, second minimum, third minimum and fourth minimum edge-Szeged indices. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：94 / 106

页数：13

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