{"title":"具有相同独立支配数的单环图的刻画","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":3,"journal":{"name":"ACS Applied Electronic Materials","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":3,\"journal\":{\"name\":\"ACS Applied Electronic Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.3000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Electronic Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.12988/ams.2023.917395\",\"RegionNum\":3,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Electronic Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.12988/ams.2023.917395","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
A characterization of unicyclic graphs with the same independent domination number
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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