{"title":"The Average Size of Independent Sets in Unicyclic Graphs","authors":"Zuwen Luo, Kexiang Xu, A. Cevik, I. Gutman","doi":"10.47443/cm.2022.051","DOIUrl":null,"url":null,"abstract":"The average size of independent sets of a graph ( avi ) is considered. It can be viewed as the logarithmic derivative of the independence polynomial at 1 . Lower and upper bounds on avi for unicyclic graphs of a given order are determined, and the respective extremal graphs are given. The unicyclic graphs that maximize (minimize) avi coincide with those that maximize (minimize, respectively) the number of independent sets.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.47443/cm.2022.051","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
The average size of independent sets of a graph ( avi ) is considered. It can be viewed as the logarithmic derivative of the independence polynomial at 1 . Lower and upper bounds on avi for unicyclic graphs of a given order are determined, and the respective extremal graphs are given. The unicyclic graphs that maximize (minimize) avi coincide with those that maximize (minimize, respectively) the number of independent sets.
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