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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-09 DOI:10.1515/math-2023-0179

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

{"title":"On the maximum atom-bond sum-connectivity index of graphs","authors":"Tariq Alraqad, Hicham Saber, Akbar Ali, Abeer M. Albalahi","doi":"10.1515/math-2023-0179","DOIUrl":null,"url":null,"abstract":"The atom-bond sum-connectivity (ABS) index of a graph <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>G</m:mi> </m:math> G with edges <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi>e</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo form=\"prefix\">,</m:mo> <m:mrow> <m:mo>…</m:mo> </m:mrow> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi>e</m:mi> </m:mrow> <m:mrow> <m:mi>m</m:mi> </m:mrow> </m:msub> </m:math> {e}_{1},\\ldots ,{e}_{m} is the sum of the numbers <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msqrt> <m:mrow> <m:mn>1</m:mn> <m:mo>−</m:mo> <m:mn>2</m:mn> <m:msup> <m:mrow> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi>d</m:mi> </m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi>e</m:mi> </m:mrow> <m:mrow> <m:mi>i</m:mi> </m:mrow> </m:msub> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:mn>2</m:mn> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> <m:mrow> <m:mo>−</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msup> </m:mrow> </m:msqrt> </m:math> \\sqrt{1-2{\\left({d}_{{e}_{i}}+2)}^{-1}} over <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mn>1</m:mn> <m:mo>≤</m:mo> <m:mi>i</m:mi> <m:mo>≤</m:mo> <m:mi>m</m:mi> </m:math> 1\\le i\\le m , where <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi>d</m:mi> </m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi>e</m:mi> </m:mrow> <m:mrow> <m:mi>i</m:mi> </m:mrow> </m:msub> </m:mrow> </m:msub> </m:math> {d}_{{e}_{i}} is the number of edges adjacent to <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi>e</m:mi> </m:mrow> <m:mrow> <m:mi>i</m:mi> </m:mrow> </m:msub> </m:math> {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.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/math-2023-0179","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

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.

查看原文本刊更多论文

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。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.