{"title":"零碎克制支配","authors":"P. Vijayalakshmi, K. Karuppasamy, Tiji Thomas","doi":"10.1142/s1793830924500046","DOIUrl":null,"url":null,"abstract":"Let G be a graph with a set of V vertices and a set of E edges. A function [Formula: see text] is called a restrained dominating function (RDF) of G if, for every [Formula: see text] [Formula: see text]. A restrained dominating function f of a graph G is called minimal (MRDF) if, for all functions [Formula: see text] such that [Formula: see text] and g(v) [Formula: see text] f(v) for at least one [Formula: see text] g is not a RDF. The fractional restrained domination number [Formula: see text] is defined as follows: [Formula: see text]: f is an MRDF of G[Formula: see text] where [Formula: see text].","PeriodicalId":504044,"journal":{"name":"Discrete Mathematics, Algorithms and Applications","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fractional restrained domination\",\"authors\":\"P. Vijayalakshmi, K. Karuppasamy, Tiji Thomas\",\"doi\":\"10.1142/s1793830924500046\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let G be a graph with a set of V vertices and a set of E edges. A function [Formula: see text] is called a restrained dominating function (RDF) of G if, for every [Formula: see text] [Formula: see text]. A restrained dominating function f of a graph G is called minimal (MRDF) if, for all functions [Formula: see text] such that [Formula: see text] and g(v) [Formula: see text] f(v) for at least one [Formula: see text] g is not a RDF. The fractional restrained domination number [Formula: see text] is defined as follows: [Formula: see text]: f is an MRDF of G[Formula: see text] where [Formula: see text].\",\"PeriodicalId\":504044,\"journal\":{\"name\":\"Discrete Mathematics, Algorithms and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-02-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics, Algorithms and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s1793830924500046\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics, Algorithms and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s1793830924500046","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
设 G 是一个有 V 个顶点和 E 条边的图。如果对于每个函数 [公式：见正文] [公式：见正文]，G 的一个函数 [公式：见正文] 称为限制支配函数 (RDF)。如果对于所有函数 [公式：见正文]，且 g(v) [公式：见正文] f(v) 至少有一个 [公式：见正文] g 不是 RDF，则图 G 的限制支配函数 f 称为最小值（MRDF）。小数约束支配数[式：见正文]定义如下：[公式：见正文]：f 是 G 的 MRDF[公式：见正文]，其中[公式：见正文]。
Let G be a graph with a set of V vertices and a set of E edges. A function [Formula: see text] is called a restrained dominating function (RDF) of G if, for every [Formula: see text] [Formula: see text]. A restrained dominating function f of a graph G is called minimal (MRDF) if, for all functions [Formula: see text] such that [Formula: see text] and g(v) [Formula: see text] f(v) for at least one [Formula: see text] g is not a RDF. The fractional restrained domination number [Formula: see text] is defined as follows: [Formula: see text]: f is an MRDF of G[Formula: see text] where [Formula: see text].
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