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Locating-Total Domination in Grid Graphs

  • Jia GuoEmail author
  • Zhuo Li
  • Mei Lu
Article
  • 17 Downloads

Abstract

Let \(G=(V,E)\) be a graph with no isolated vertex. A subset \(S\subseteq V(G)\) is a total dominating set of graph G if every vertex in V(G) is adjacent to at least one vertex in S. A total dominating set S of graph G is a locating-total dominating set if for every pair of distinct vertices \(u_1\) and \(u_2\) in \(V(G)-S\), \(N(u_1)\cap S\ne N(u_2)\cap S\). The locating-total domination number of graph G, denoted by \(\gamma _t^L(G)\), is the minimum cardinality of a locating-total dominating set of G. In this paper, we investigate the bounds of locating-total domination number of grid graphs.

Keywords

Locating-total dominating set Locating-total domination number Cartesian product Grid graph 

Mathematics Subject Classification

05C50 15A18 

Notes

Acknowledgements

This work is partially supported by National Natural Science Foundation of China (Nos. 11801450, 11771247). In addition, the authors are thankful to the anonymous referees for their useful comments and suggestions.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.College of ScienceNorthwest A&F UniversityYanglingPeople’s Republic of China
  2. 2.Department of Mathematical SciencesTsinghua UniversityBeijingPeople’s Republic of China

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