{"title":"Domination Number of Square of Cartesian Products of Cycles","authors":"M. Alishahi, Sakineh Hoseini Shalmaee","doi":"10.4236/OJDM.2015.54008","DOIUrl":null,"url":null,"abstract":"A set is a dominating set of G if every vertex of is adjacent to at least one vertex of S. The cardinality of the smallest \ndominating set of G is called the \ndomination number of G. The square G2 of a graph G is obtained from G by adding new edges between every two vertices having distance 2 \nin G. In this paper we study the \ndomination number of square of graphs, find a bound for domination number of \nsquare of Cartesian product of cycles, and find the exact value for some of \nthem.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"05 1","pages":"88-94"},"PeriodicalIF":0.0000,"publicationDate":"2015-08-12","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.2015.54008","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
A set is a dominating set of G if every vertex of is adjacent to at least one vertex of S. The cardinality of the smallest
dominating set of G is called the
domination number of G. The square G2 of a graph G is obtained from G by adding new edges between every two vertices having distance 2
in G. In this paper we study the
domination number of square of graphs, find a bound for domination number of
square of Cartesian product of cycles, and find the exact value for some of
them.
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