On the total domination subdivision number in some classes of graphs

AbstractA set S of vertices of a graph G=(V,E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination numberγt(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number$\mathrm {sd}_{\gamma_{t}}(G)$ is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. In this paper we prove that $\mathrm {sd}_{\gamma_{t}}(G)\leq\gamma_{t}(G)+1$ for some classes of graphs.