{"title":"关于图的k元组支配数的注意事项","authors":"Abel Cabrera Martínez","doi":"10.26493/1855-3974.2600.dcc","DOIUrl":null,"url":null,"abstract":"In a graph G, a vertex dominates itself and its neighbours. A set D ⊆ V (G) is said to be a k-tuple dominating set of G if D dominates every vertex of G at least k times. The minimum cardinality among all k-tuple dominating sets is the k-tuple domination number of G. In this note, we provide new bounds on this parameter. Some of these bounds generalize other ones that have been given for the case k = 2.","PeriodicalId":8402,"journal":{"name":"Ars Math. Contemp.","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"A note on the k-tuple domination number of graphs\",\"authors\":\"Abel Cabrera Martínez\",\"doi\":\"10.26493/1855-3974.2600.dcc\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In a graph G, a vertex dominates itself and its neighbours. A set D ⊆ V (G) is said to be a k-tuple dominating set of G if D dominates every vertex of G at least k times. The minimum cardinality among all k-tuple dominating sets is the k-tuple domination number of G. In this note, we provide new bounds on this parameter. Some of these bounds generalize other ones that have been given for the case k = 2.\",\"PeriodicalId\":8402,\"journal\":{\"name\":\"Ars Math. Contemp.\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-04-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ars Math. Contemp.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26493/1855-3974.2600.dcc\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ars Math. Contemp.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26493/1855-3974.2600.dcc","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In a graph G, a vertex dominates itself and its neighbours. A set D ⊆ V (G) is said to be a k-tuple dominating set of G if D dominates every vertex of G at least k times. The minimum cardinality among all k-tuple dominating sets is the k-tuple domination number of G. In this note, we provide new bounds on this parameter. Some of these bounds generalize other ones that have been given for the case k = 2.
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