A NEW BOUND FOR DISTANCE DOMINATION NUMBER OF CONNECTED BIPARTITE GRAPHS

A vertex u in graph G dominates itself and all its neighbers and also u k- dominates itself and all vertices by distance within k from u. A set D ⊆ V (G) k-dominates G if each vertex in G is k-dominated by at least one vertex in D and is called a distance k-dominating set of G. The minimum cardinality among all distance k-dominating sets of G is called the distance k-domination number of G. We will give an upper bound for distance k-domination number of connected bipartite graphs.