On the difference between the (revised) Szeged index and the Wiener index of cacti

被引：17
|
作者：
Klavzar, Sandi [1 ,2 ,3 ]
Li, Shuchao [4 ]
Zhang, Huihui [5 ]
机构：
[1] Univ Ljubljana, Fac Math & Phys, Ljubljana, Slovenia
[2] Univ Maribor, Fac Nat Sci & Math, Maribor, Slovenia
[3] Inst Math Phys & Mech, Ljubljana, Slovenia
[4] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Hubei, Peoples R China
[5] Luoyang Normal Univ, Dept Math, Luoyang 471002, Peoples R China
来源：
DISCRETE APPLIED MATHEMATICS | 2018年 / 247卷
基金：
中国国家自然科学基金;
关键词：
Wiener index; Szeged index; Revised Szeged index; Extremal problem; Isometric cycle; BIPARTITE GRAPHS; BICYCLIC GRAPHS; DISTANCE; SYSTEMS; TREES;
D O I：
10.1016/j.dam.2018.03.038
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A connected graph is said to be a cactus if each of its blocks is either a cycle or an edge. Let cen be the set of all n-vertex cacti with circumference at least 4, and let l(n,k) be the set of all n -vertex cacti containing exactly k >= 1 cycles where n >= 3k + 1. In this paper, lower bounds on the difference between the (revised) Szeged index and Wiener index of graphs l(n) (resp.l(n,k)) are proved. The minimum and the second minimum values on the difference between the Szeged index and Wiener index of graphs among,e are determined. The bound on the minimum value is strengthened in the bipartite case. A lower bound on the difference between the revised Szeged index and Wiener index of graphs among l(n,k) is also established. Along the way the corresponding extremal graphs are identified. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码：77 / 89
页数：13
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