{"title":"意大利人对树木的控制受到了限制","authors":"Kijung Kim","doi":"10.1080/23799927.2021.1973567","DOIUrl":null,"url":null,"abstract":"Let be a graph. A subset D of V is a restrained dominating set if every vertex in is adjacent to a vertex in D and to a vertex in . The restrained domination number, denoted by , is the smallest cardinality of a restrained dominating set of G. A function is a restrained Italian dominating function on G if (i) for each vertex for which , it holds that , (ii) the subgraph induced by has no isolated vertices. The restrained Italian domination number, denoted by , is the minimum weight taken over all restrained Italian dominating functions of G. It is known that for any graph G. In this paper, we characterize the trees T for which , and we also characterize the trees T for which .","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2021-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Restrained Italian domination in trees\",\"authors\":\"Kijung Kim\",\"doi\":\"10.1080/23799927.2021.1973567\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let be a graph. A subset D of V is a restrained dominating set if every vertex in is adjacent to a vertex in D and to a vertex in . The restrained domination number, denoted by , is the smallest cardinality of a restrained dominating set of G. A function is a restrained Italian dominating function on G if (i) for each vertex for which , it holds that , (ii) the subgraph induced by has no isolated vertices. The restrained Italian domination number, denoted by , is the minimum weight taken over all restrained Italian dominating functions of G. It is known that for any graph G. In this paper, we characterize the trees T for which , and we also characterize the trees T for which .\",\"PeriodicalId\":37216,\"journal\":{\"name\":\"International Journal of Computer Mathematics: Computer Systems Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2021-01-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Computer Mathematics: Computer Systems Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/23799927.2021.1973567\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Computer Mathematics: Computer Systems Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/23799927.2021.1973567","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
Let be a graph. A subset D of V is a restrained dominating set if every vertex in is adjacent to a vertex in D and to a vertex in . The restrained domination number, denoted by , is the smallest cardinality of a restrained dominating set of G. A function is a restrained Italian dominating function on G if (i) for each vertex for which , it holds that , (ii) the subgraph induced by has no isolated vertices. The restrained Italian domination number, denoted by , is the minimum weight taken over all restrained Italian dominating functions of G. It is known that for any graph G. In this paper, we characterize the trees T for which , and we also characterize the trees T for which .
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