{"title":"Resolution of Yan's Conjecture on Entropy of Graphs","authors":"Stijn Cambie, Matteo Mazzamurro","doi":"10.46793/match.89-2.389c","DOIUrl":null,"url":null,"abstract":"The first degree-based entropy of a graph is the Shannon entropy of its degree sequence normalized by the degree sum. In this paper, we characterize the connected graphs with given order n and size m that minimize the first degree-based entropy whenever n − 1 ≤ m ≤ 2 n − 3 , thus extending and proving a conjecture by Yan.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"1 1","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Match-Communications in Mathematical and in Computer Chemistry","FirstCategoryId":"92","ListUrlMain":"https://doi.org/10.46793/match.89-2.389c","RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 2
Abstract
The first degree-based entropy of a graph is the Shannon entropy of its degree sequence normalized by the degree sum. In this paper, we characterize the connected graphs with given order n and size m that minimize the first degree-based entropy whenever n − 1 ≤ m ≤ 2 n − 3 , thus extending and proving a conjecture by Yan.
期刊介绍：
MATCH Communications in Mathematical and in Computer Chemistry publishes papers of original research as well as reviews on chemically important mathematical results and non-routine applications of mathematical techniques to chemical problems. A paper acceptable for publication must contain non-trivial mathematics or communicate non-routine computer-based procedures AND have a clear connection to chemistry. Papers are published without any processing or publication charge.
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