{"title":"单环图中独立集的平均大小","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":"{\"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}","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}
The Average Size of Independent Sets in Unicyclic Graphs
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.
分享
京公网安备 11010802042870号
京ICP备2023020795号-1
求助内容：
应助结果提醒方式：
扫码关注我们
