{"title":"图中若干次支配集的最小交集","authors":"Anna Kosiorowska, Adrian Michalski, Iwona W�och","doi":"10.7494/opmath.2023.43.6.813","DOIUrl":null,"url":null,"abstract":"In this paper we consider secondary dominating sets, also named as \\((1,k)\\)-dominating sets, introduced by Hedetniemi et al. in 2008. In particular, we study intersections of the \\((1,1)\\)-dominating sets and proper \\((1,2)\\)-dominating sets. We introduce \\((1,\\overline{2})\\)-intersection index as the minimum possible cardinality of such intersection and determine its value for some classes of graphs.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On minimum intersections of certain secondary dominating sets in graphs\",\"authors\":\"Anna Kosiorowska, Adrian Michalski, Iwona W�och\",\"doi\":\"10.7494/opmath.2023.43.6.813\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we consider secondary dominating sets, also named as \\\\((1,k)\\\\)-dominating sets, introduced by Hedetniemi et al. in 2008. In particular, we study intersections of the \\\\((1,1)\\\\)-dominating sets and proper \\\\((1,2)\\\\)-dominating sets. We introduce \\\\((1,\\\\overline{2})\\\\)-intersection index as the minimum possible cardinality of such intersection and determine its value for some classes of graphs.\",\"PeriodicalId\":45563,\"journal\":{\"name\":\"Opuscula Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Opuscula Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7494/opmath.2023.43.6.813\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Opuscula Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7494/opmath.2023.43.6.813","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
On minimum intersections of certain secondary dominating sets in graphs
In this paper we consider secondary dominating sets, also named as \((1,k)\)-dominating sets, introduced by Hedetniemi et al. in 2008. In particular, we study intersections of the \((1,1)\)-dominating sets and proper \((1,2)\)-dominating sets. We introduce \((1,\overline{2})\)-intersection index as the minimum possible cardinality of such intersection and determine its value for some classes of graphs.
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