Locating-Total Domination in Grid Graphs
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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.
KeywordsLocating-total dominating set Locating-total domination number Cartesian product Grid graph
Mathematics Subject Classification05C50 15A18
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.