Abstract
A set S⊆V of vertices in a graph G=(V,E) without isolated vertices is a total dominating set if every vertex of V 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 numbersdγt(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 sdγt(G)≤α′(G)+1 for some classes of graphs where α′(G) is the maximum cardinality of a matching of G.
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