A 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 number gamma(t)(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number 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 for every simple connected graph G of order n >= 3, sd(gamma t)(G) <= 3 + min{d(2)(v); v is an element of V and d(v) >= 2} where d(2)(v) is the number of vertices of G at distance 2 from v.
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