Yuehan Wu , Chengxi Hong , Peifang Fu , Wenshui Lin
{"title":"具有最大逆和 indeg 指数的大树没有阶数为 2 或 3 的顶点","authors":"Yuehan Wu , Chengxi Hong , Peifang Fu , Wenshui Lin","doi":"10.1016/j.dam.2024.09.006","DOIUrl":null,"url":null,"abstract":"<div><p>The inverse sum indeg (<span><math><mrow><mi>I</mi><mi>S</mi><mi>I</mi></mrow></math></span>) index has attracted more and more attentions, because of its significant applications in chemistry. A basic problem in the study of this topological index is the characterization trees with maximal <span><math><mrow><mi>I</mi><mi>S</mi><mi>I</mi></mrow></math></span> value. Let <span><math><mi>T</mi></math></span> be such a tree of order <span><math><mrow><mi>n</mi><mo>≥</mo><mn>20</mn></mrow></math></span>. Recently, Lin et al. (2022) claimed that <span><math><mi>T</mi></math></span> has no vertices of degree 2. However, errors were found in their proofs. Since this result is quite important, we give a correction to the proof. Furthermore, we extend the result by proving that <span><math><mi>T</mi></math></span> has no vertices of degree 2 or 3 if <span><math><mrow><mi>n</mi><mo>≥</mo><mn>58</mn></mrow></math></span>.</p></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"360 ","pages":"Pages 131-138"},"PeriodicalIF":1.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0166218X24003949/pdfft?md5=6f31123f073d46ec4f365b5d99d2a66f&pid=1-s2.0-S0166218X24003949-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Large trees with maximal inverse sum indeg index have no vertices of degree 2 or 3\",\"authors\":\"Yuehan Wu , Chengxi Hong , Peifang Fu , Wenshui Lin\",\"doi\":\"10.1016/j.dam.2024.09.006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The inverse sum indeg (<span><math><mrow><mi>I</mi><mi>S</mi><mi>I</mi></mrow></math></span>) index has attracted more and more attentions, because of its significant applications in chemistry. A basic problem in the study of this topological index is the characterization trees with maximal <span><math><mrow><mi>I</mi><mi>S</mi><mi>I</mi></mrow></math></span> value. Let <span><math><mi>T</mi></math></span> be such a tree of order <span><math><mrow><mi>n</mi><mo>≥</mo><mn>20</mn></mrow></math></span>. Recently, Lin et al. (2022) claimed that <span><math><mi>T</mi></math></span> has no vertices of degree 2. However, errors were found in their proofs. Since this result is quite important, we give a correction to the proof. Furthermore, we extend the result by proving that <span><math><mi>T</mi></math></span> has no vertices of degree 2 or 3 if <span><math><mrow><mi>n</mi><mo>≥</mo><mn>58</mn></mrow></math></span>.</p></div>\",\"PeriodicalId\":50573,\"journal\":{\"name\":\"Discrete Applied Mathematics\",\"volume\":\"360 \",\"pages\":\"Pages 131-138\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0166218X24003949/pdfft?md5=6f31123f073d46ec4f365b5d99d2a66f&pid=1-s2.0-S0166218X24003949-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0166218X24003949\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166218X24003949","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
由于其在化学中的重要应用，逆和指数（ISI）受到越来越多的关注。研究该拓扑指数的一个基本问题是找出 ISI 值最大的树的特征。设 T 是这样一棵阶数 n≥20 的树。最近，Lin 等人（2022 年）声称 T 没有阶数为 2 的顶点。由于这一结果相当重要，我们对证明进行了修正。此外，我们还扩展了这一结果，证明如果 n≥58 则 T 没有阶数为 2 或 3 的顶点。
Large trees with maximal inverse sum indeg index have no vertices of degree 2 or 3
The inverse sum indeg () index has attracted more and more attentions, because of its significant applications in chemistry. A basic problem in the study of this topological index is the characterization trees with maximal value. Let be such a tree of order . Recently, Lin et al. (2022) claimed that has no vertices of degree 2. However, errors were found in their proofs. Since this result is quite important, we give a correction to the proof. Furthermore, we extend the result by proving that has no vertices of degree 2 or 3 if .
期刊介绍：
The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal.
Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
