Some New Results on Double Domination in Graphs

Abstract:

      Each vertex of a graph G = (V, E) is said to dominate every vertex in its closed neighborhood. A set S?V is a double dominating set for G if each vertex in V is dominated by at least two vertices in S. The smallest cardinality of a double dominating set is called the double dominating number dd(G). In this paper, new relationships between dd(G) and other domination parameters are explored and some results of [1] are extended. Furthermore, we give the Nordhaus-Gaddum-type results for double dominating number.