{"title":"Bounds on the domination number and the metric dimension of co-normal product of graphs.","authors":"Imran Javaid, Shahid Ur Rehman, Muhammad Imran","doi":"10.1186/s13660-018-1752-5","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper, we establish bounds on the domination number and the metric dimension of the co-normal product graph <math><msub><mi>G</mi><mi>H</mi></msub></math> of two simple graphs <i>G</i> and <i>H</i> in terms of parameters associated with <i>G</i> and <i>H</i>. We also give conditions on the graphs <i>G</i> and <i>H</i> for which the domination number of <math><msub><mi>G</mi><mi>H</mi></msub></math> is 1, 2, and the domination number of <i>G</i>. Moreover, we give formulas for the metric dimension of the co-normal product <math><msub><mi>G</mi><mi>H</mi></msub></math> of some families of graphs <i>G</i> and <i>H</i> as a function of associated parameters of <i>G</i> and <i>H</i>.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"162"},"PeriodicalIF":1.6000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1752-5","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Inequalities and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13660-018-1752-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2018/7/4 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 2
Abstract
In this paper, we establish bounds on the domination number and the metric dimension of the co-normal product graph of two simple graphs G and H in terms of parameters associated with G and H. We also give conditions on the graphs G and H for which the domination number of is 1, 2, and the domination number of G. Moreover, we give formulas for the metric dimension of the co-normal product of some families of graphs G and H as a function of associated parameters of G and H.
期刊介绍：
The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.
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