{"title":"A characterization of unicyclic graphs with the same independent domination number","authors":"Min-Jen Jou, Jenq-Jong Lin, Guan-Yu Lin","doi":"10.12988/ams.2023.917395","DOIUrl":null,"url":null,"abstract":"A set D of vertices of G is an independent dominating set if no two vertices of D are adjacent and every vertex not in D is adjacent to at lest one vertex in D . The independent domination number of a graph G , denoted by i ( G ), is the minimum cardinality of an independent dominating set in G . A unicyclic graph is a connected graph containing exactly one cycle. For k ≥ 1, let H ( k ) be the set of unicyclic graphs H satisfying i ( H ) = k . In this paper, we provide a constructive characterization of H ( k ) for all k ≥ 1.","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":null,"pages":null},"PeriodicalIF":3.6000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Models & Methods in Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.12988/ams.2023.917395","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
A set D of vertices of G is an independent dominating set if no two vertices of D are adjacent and every vertex not in D is adjacent to at lest one vertex in D . The independent domination number of a graph G , denoted by i ( G ), is the minimum cardinality of an independent dominating set in G . A unicyclic graph is a connected graph containing exactly one cycle. For k ≥ 1, let H ( k ) be the set of unicyclic graphs H satisfying i ( H ) = k . In this paper, we provide a constructive characterization of H ( k ) for all k ≥ 1.
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