{"title":"On the trees with given matching number and the modified first Zagreb connection index","authors":"Sadia Noureen, A. A. Bhatti","doi":"10.22052/IJMC.2021.242169.1554","DOIUrl":null,"url":null,"abstract":"The modified first Zagreb connection index ZC∗1 for a graph G is defined as ZC∗1 (G) = sum v∈V (G) dvτv , where dv is the degree of the vertex v and τv denotes the connection number of v (that is, the number of vertices at the distance 2 from the vertex v). Let Tn,α be the class of trees with order n and matching number α such that n > 2α−1. In this paper, we obtain the lower bounds on the modified first Zagreb connection index of trees belonging to the class Tn,α, for 2α − 1 < n < 3α + 2.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":"109 1","pages":"127-138"},"PeriodicalIF":1.0000,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Iranian journal of mathematical chemistry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22052/IJMC.2021.242169.1554","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 1
Abstract
The modified first Zagreb connection index ZC∗1 for a graph G is defined as ZC∗1 (G) = sum v∈V (G) dvτv , where dv is the degree of the vertex v and τv denotes the connection number of v (that is, the number of vertices at the distance 2 from the vertex v). Let Tn,α be the class of trees with order n and matching number α such that n > 2α−1. In this paper, we obtain the lower bounds on the modified first Zagreb connection index of trees belonging to the class Tn,α, for 2α − 1 < n < 3α + 2.
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