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 introduce an upper bound of the difference between γt(G) and α'(G): We also characterize every tree T with γt(T) ⩽ α'(T); and give a family of graphs with γt(G) ⩽ α'(G). [ABSTRACT FROM AUTHOR]