Some results on matching and total domination in graphs

Let G be a graph. A set S of vertices of G is called a total dominating set of G if every vertex of G is adjacent to at least one vertex in S. The total domination number _γt(G) and the matching number α’(G) of G are the cardinalities of the minimum total dominating set and the maximum matching of G, respectively. In this paper, we will introduce an upper bound of the difference between _γt(G) and α’(G). We will also characterize every tree T with _γt(T)≤ α’(T), and give a family of graphs with _γt(G)≤α’(G). Copyright © 2010 Akademska misao.