{"title":"中图中的规则约束支配","authors":"M.H. Muddebihal, Shobha Mahadevappa","doi":"10.15379/ijmst.v10i1.2988","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce the new concept called regular restrained domination in middle graph.A set S ? V[M(G)] is a restrained dominating set if every vertex in V-S is adjacent to a vertex in S and another vertex in V-S. Note that every graph has a restrained dominating set, since S=V is such a set. Let ?rr[M(G)] denote the size of a smallest restrained dominating set. Also we study the graph theoretic properties of ?rr[M(G)] and many bounds were obtained in terms of elements of G and its relationships with other domination parameters were found.","PeriodicalId":499708,"journal":{"name":"International journal of membrane science and technology","volume":"57 8","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Regular Restrained Domination in Middle Graph\",\"authors\":\"M.H. Muddebihal, Shobha Mahadevappa\",\"doi\":\"10.15379/ijmst.v10i1.2988\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we introduce the new concept called regular restrained domination in middle graph.A set S ? V[M(G)] is a restrained dominating set if every vertex in V-S is adjacent to a vertex in S and another vertex in V-S. Note that every graph has a restrained dominating set, since S=V is such a set. Let ?rr[M(G)] denote the size of a smallest restrained dominating set. Also we study the graph theoretic properties of ?rr[M(G)] and many bounds were obtained in terms of elements of G and its relationships with other domination parameters were found.\",\"PeriodicalId\":499708,\"journal\":{\"name\":\"International journal of membrane science and technology\",\"volume\":\"57 8\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International journal of membrane science and technology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15379/ijmst.v10i1.2988\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International journal of membrane science and technology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15379/ijmst.v10i1.2988","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, we introduce the new concept called regular restrained domination in middle graph.A set S ? V[M(G)] is a restrained dominating set if every vertex in V-S is adjacent to a vertex in S and another vertex in V-S. Note that every graph has a restrained dominating set, since S=V is such a set. Let ?rr[M(G)] denote the size of a smallest restrained dominating set. Also we study the graph theoretic properties of ?rr[M(G)] and many bounds were obtained in terms of elements of G and its relationships with other domination parameters were found.
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