极大次几何算术索引的极值树

IF 1 Q1 MATHEMATICS Discrete Mathematics Letters Pub Date : 2022-01-27 DOI:10.47443/dml.2021.s207

A. Divya, A. Manimaran

{"title":"极大次几何算术索引的极值树","authors":"A. Divya, A. Manimaran","doi":"10.47443/dml.2021.s207","DOIUrl":null,"url":null,"abstract":"Abstract For a graph G, the geometric-arithmetic index of G, denoted by GA(G), is defined as the sum of the quantities 2 √ dx × dy/(dx + dy) over all edges xy ∈ E(G). Here, dx indicates the vertex degree of x. For every tree T of order n ≥ 3, Vukičević and Furtula [J. Math. Chem. 46 (2009) 1369–1376] demonstrated that GA(T ) ≤ 4 √ 2 3 + (n − 3). This result is extended in the present paper. Particularly, for any tree T of order n ≥ 5 and maximum degree ∆, it is proved that","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2022-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Extremal Trees for the Geometric-Arithmetic Index with the Maximum Degree\",\"authors\":\"A. Divya, A. Manimaran\",\"doi\":\"10.47443/dml.2021.s207\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract For a graph G, the geometric-arithmetic index of G, denoted by GA(G), is defined as the sum of the quantities 2 √ dx × dy/(dx + dy) over all edges xy ∈ E(G). Here, dx indicates the vertex degree of x. For every tree T of order n ≥ 3, Vukičević and Furtula [J. Math. Chem. 46 (2009) 1369–1376] demonstrated that GA(T ) ≤ 4 √ 2 3 + (n − 3). This result is extended in the present paper. Particularly, for any tree T of order n ≥ 5 and maximum degree ∆, it is proved that\",\"PeriodicalId\":36023,\"journal\":{\"name\":\"Discrete Mathematics Letters\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2022-01-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics Letters\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.47443/dml.2021.s207\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics Letters","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47443/dml.2021.s207","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

摘要对于图G，用GA（G）表示的G的几何算术指数被定义为所有边xy∈E（G）上的量2√dx×dy/（dx+dy）的和。这里，dx表示x的顶点度。对于n≥3阶的每棵树T，Vukičević和Furtula[J.Math.Chem.46（2009）1369–1376]证明了GA（T）≤4√2 3+（n−3）。这一结果在本文中得到了推广。特别地，对于n≥5阶且最大阶为∆的任意树T，证明了

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Extremal Trees for the Geometric-Arithmetic Index with the Maximum Degree

Abstract For a graph G, the geometric-arithmetic index of G, denoted by GA(G), is defined as the sum of the quantities 2 √ dx × dy/(dx + dy) over all edges xy ∈ E(G). Here, dx indicates the vertex degree of x. For every tree T of order n ≥ 3, Vukičević and Furtula [J. Math. Chem. 46 (2009) 1369–1376] demonstrated that GA(T ) ≤ 4 √ 2 3 + (n − 3). This result is extended in the present paper. Particularly, for any tree T of order n ≥ 5 and maximum degree ∆, it is proved that

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊