{"title":"On the Number of All Substructures Containing at Most Four Edges","authors":"S. Gong, Liping Zhang, Changbao Su","doi":"10.46793/match.89-2.327g","DOIUrl":null,"url":null,"abstract":"Let G be a simple graph with order n , n ≥ 5, and adjacency matrix A ( G ). In this paper, we determine the number of all substructures having at most four edges in terms of its adjacency matrix A ( G ) together with some graph invariants determined by A ( G ). Then, as applications, we provide an algebraic expression for the second Zagreb index and || A 4 || of a graph.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Match-Communications in Mathematical and in Computer Chemistry","FirstCategoryId":"92","ListUrlMain":"https://doi.org/10.46793/match.89-2.327g","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: 0
Abstract
Let G be a simple graph with order n , n ≥ 5, and adjacency matrix A ( G ). In this paper, we determine the number of all substructures having at most four edges in terms of its adjacency matrix A ( G ) together with some graph invariants determined by A ( G ). Then, as applications, we provide an algebraic expression for the second Zagreb index and || A 4 || of a graph.
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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