{"title":"Bounds for metric dimension and defensive k-alliance of graphs under deleted lexicographic product","authors":"K. Das, M. Tavakoli","doi":"10.22108/TOC.2019.115674.1622","DOIUrl":null,"url":null,"abstract":"Metric dimension and defensive $k$-alliance number are two distance-based graph invariants which have applications in robot navigation, quantitative analysis of secondary RNA structures, national defense and fault-tolerant computing. In this paper, some bounds for metric dimension and defensive $k$-alliance of deleted lexicographic product of graphs are presented. We also show that the bounds are sharp.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"9 1","pages":"31-39"},"PeriodicalIF":0.6000,"publicationDate":"2019-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions on Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22108/TOC.2019.115674.1622","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
Metric dimension and defensive $k$-alliance number are two distance-based graph invariants which have applications in robot navigation, quantitative analysis of secondary RNA structures, national defense and fault-tolerant computing. In this paper, some bounds for metric dimension and defensive $k$-alliance of deleted lexicographic product of graphs are presented. We also show that the bounds are sharp.
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