{"title":"关于两个有向环笛卡尔积的符号支配数","authors":"Ramy S. Shaheen","doi":"10.4236/OJDM.2015.53005","DOIUrl":null,"url":null,"abstract":"Let D be a finite simple directed graph with vertex set V(D) and arc set A(D). A function is called a signed dominating function (SDF) if for each vertex . The weight of f is defined by . The signed domination number of a digraph D is . Let Cm × Cn denotes the cartesian product of directed cycles of length m and n. In this paper, we determine the exact values of gs(Cm × Cn) for m = 8, 9, 10 and arbitrary n. Also, we give the exact value of gs(Cm × Cn) when m, (mod 3) and bounds for otherwise.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"24 1","pages":"54-64"},"PeriodicalIF":0.0000,"publicationDate":"2015-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On the Signed Domination Number of the Cartesian Product of Two Directed Cycles\",\"authors\":\"Ramy S. Shaheen\",\"doi\":\"10.4236/OJDM.2015.53005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let D be a finite simple directed graph with vertex set V(D) and arc set A(D). A function is called a signed dominating function (SDF) if for each vertex . The weight of f is defined by . The signed domination number of a digraph D is . Let Cm × Cn denotes the cartesian product of directed cycles of length m and n. In this paper, we determine the exact values of gs(Cm × Cn) for m = 8, 9, 10 and arbitrary n. Also, we give the exact value of gs(Cm × Cn) when m, (mod 3) and bounds for otherwise.\",\"PeriodicalId\":61712,\"journal\":{\"name\":\"离散数学期刊(英文)\",\"volume\":\"24 1\",\"pages\":\"54-64\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-07-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"离散数学期刊(英文)\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://doi.org/10.4236/OJDM.2015.53005\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"离散数学期刊(英文)","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.4236/OJDM.2015.53005","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the Signed Domination Number of the Cartesian Product of Two Directed Cycles
Let D be a finite simple directed graph with vertex set V(D) and arc set A(D). A function is called a signed dominating function (SDF) if for each vertex . The weight of f is defined by . The signed domination number of a digraph D is . Let Cm × Cn denotes the cartesian product of directed cycles of length m and n. In this paper, we determine the exact values of gs(Cm × Cn) for m = 8, 9, 10 and arbitrary n. Also, we give the exact value of gs(Cm × Cn) when m, (mod 3) and bounds for otherwise.
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