On the Total Domination Number of Graphs with Minimum Degree at Least Three

Let G be a simple graph with no isolated vertices. A set S of vertices of G is a total dominating set if every vertex of G is adjacent to some vertex in S. The total domination number of G, denoted by γ t (G), is the minimum cardinality of a total dominating set of G. It is shown that if G is a graph of order n with minimum degree at least 3, then γ t (G)≤n/2. Thus a conjecture of Favaron, Henning, Mynhart and Puech is settled in the affirmative.