On the maximum atom-bond sum-connectivity index of graphs

IF 1 4区数学 Q1 MATHEMATICS Open Mathematics Pub Date : 2024-02-09 DOI:10.1515/math-2023-0179

Tariq Alraqad, Hicham Saber, Akbar Ali, Abeer M. Albalahi

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引用次数: 0

Abstract

The atom-bond sum-connectivity (ABS) index of a graph

with edges

e 1 , … , e m

{e}_{1},\ldots ,{e}_{m}

is the sum of the numbers

1 − 2 ( d e i + 2 ) − 1

\sqrt{1-2{\left({d}_{{e}_{i}}+2)}^{-1}}

over

1 ≤ i ≤ m

1\le i\le m

, where

d e i

{d}_{{e}_{i}}

is the number of edges adjacent to

e i

{e}_{i}

. In this article, we study the maximum values of the ABS index over graphs with given parameters. More specifically, we determine the maximum ABS index of connected graphs of a given order with a fixed (i) minimum degree, (ii) maximum degree, (iii) chromatic number, (iv) independence number, or (v) number of pendent vertices. We also characterize the graphs attaining the maximum ABS values in all of these classes.

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论图形的最大原子键和连接指数

具有边 e 1 , ... , e m {e}_{1},\ldots ,{e}_{m} 的图 G G 的原子-键总和-连通性（ABS）指数是 , e m {e}_{1},\ldots ,{e}_{m} 是 1 - 2 ( d e i + 2 ) - 1 \sqrt{1-2\{left({d}_{e}_{i}+2)}^{-1}}}在 1 ≤ i ≤ m 1\le i\le m 上的数字之和，其中 d e i {d}_{e}_{i}} 是与 e i {e}_{i} 相邻的边的数目。在本文中，我们将研究具有给定参数的图中 ABS 指数的最大值。更具体地说，我们确定了具有固定(i)最小度、(ii)最大度、(iii)色度数、(iv)独立性数或(v)下垂顶点数的给定阶数连通图的最大 ABS 指数。我们还描述了在所有这些类别中达到最大 ABS 值的图的特征。

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

Open Mathematics MATHEMATICS-

CiteScore

2.40

自引率

5.90%

发文量

审稿时长

16 weeks

期刊介绍： Open Mathematics - formerly Central European Journal of Mathematics Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant, original and relevant works in all areas of mathematics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, language-correction services, no space constraints and immediate publication. Open Mathematics is listed in Thomson Reuters - Current Contents/Physical, Chemical and Earth Sciences. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind. Aims and Scope The journal aims at presenting high-impact and relevant research on topics across the full span of mathematics. Coverage includes: