LAUSR

Let $$G=(V,E)$$ G = ( V , E ) be a graph with no isolated vertex. A subset $$S\subseteq V(G)$$ S ⊆ 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 $$u_1$$ u 1 and $$u_2$$ u 2 in $$V(G)-S$$ V ( G ) - S , $$N(u_1)\cap S\ne N(u_2)\cap S$$ N ( u 1 ) ∩ S ≠ N ( u 2 ) ∩ S . The locating-total domination number of graph G , denoted by $$\gamma _t^L(G)$$ γ 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.