Lower bound for the Sombor index of trees with a given total domination number

IF 2.6 3区数学 Computational and Applied Mathematics Pub Date : 2024-08-03 DOI:10.1007/s40314-024-02871-8

Xiaoling Sun, Jianwei Du, Yinzhen Mei

引用次数: 0

Abstract

Recently, finding extremal structures of graphs on Sombor index has received a lot of attention. The Sombor (SO) index of a graph G is defined by the sum of weights \(\sqrt{deg_{G}(u)^{2}+deg_{G}(v)^{2}}\) over all edges uv of G, where \(deg_{G}(u)\) stands for the degree of vertex u in G. In this article, we obtain a lower bound on Sombor index of trees with a given order and total domination number, and characterize the trees achieving the bound.

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具有给定总支配数的树木的松博指数下限

最近，寻找图的极值结构（Sombor index）受到了广泛关注。图 G 的 Sombor（SO）指数定义为 G 中所有边 uv 的权重总和（\sqrt{deg_{G}(u)^{2}+deg_{G}(v)^{2}}/），其中 \(deg_{G}(u)\)表示顶点 u 在 G 中的度数。在本文中，我们得到了具有给定阶数和总支配数的树的松博指数下限，并描述了达到下限的树的特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational and Applied Mathematics MATHEMATICS, APPLIED-

自引率

11.50%

发文量

352

期刊介绍： Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics). The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.