On the Total Domination Subdivision Numbers of Grid Graphs
نویسندگان
چکیده
A set S of vertices in a graph G(V,E) is called a total dominating set if every vertex v ∈ V is adjacent to an element of S. The total domination number of a graph G denoted by γt(G) is the minimum cardinality of a total dominating set in G. Total domination subdivision number denoted by sdγt is the minimum number of edges that must be subdivided to increase the total domination number. Here we investigate the problem of total domination subdivision numbers of grid graphs Pm,n and determine the total domination subdivision numbers of grid graphs Pm,n for m = 2, 3 and 4, and n ≥ 2. Also Haynes et al. [4] showed that 1 ≤ sdγt(Pm,n) ≤ 4 for any grid graph Pm,n. We improve this bound and prove that sdγt(Pm,n) ≤ 3. Mathematics Subject Classification: 05C69
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