General sum-connectivity index of unicyclic graphs with given maximum degree

被引：0

作者：

Swartz, Elize ^{[1
]}

Vetrik, Tomas ^{[1
]}

机构：

[1] Univ Free State, Dept Math & Appl Math, POB 339, ZA-9300 Bloemfontein, South Africa

来源：

DISCRETE APPLIED MATHEMATICS | 2025年 / 366卷

基金：

新加坡国家研究基金会;

关键词：

General sum-connectivity index; Unicyclic graph; Maximum degree; TREES;

D O I：

10.1016/j.dam.2025.01.033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a is an element of R, the general sum-connectivity index chi(a) of a graph G is defined as chi(a)(G) = & sum;(uv is an element of E)((G)())[d(G)(u)+dG(v)](a), where E(G) is the set of edges of G, and d(G)(u) and d(G)(v) are the degrees of vertices u and v, respectively. Among unicyclic graphs with given number of vertices and maximum degree, we present graphs having the largest and smallest values of chi(a), and we state cases which are still open. We also solve one of the open problems on chi(a) for trees if 0 < a < 1.

引用

页码：238 / 249

页数：12

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