DOUBLE DOMINATION NUMBER AND CONNECTIVITY OF GRAPHS

In a graph G, a vertex dominates itself and its neighbours. A subset S of V is called a dominating set in G if every vertex in V is dominated by at least one vertex in S. The domination number is the minimum cardinality of a dominating set. A set is called a double dominating set of a graph G if every vertex in V is dominated by at least two vertices in S. The minimum cardinality of a double dominating set is called double domination number of G and is denoted by dd(G). The connectivity of a connected graph G is the minimum number of vertices whose removal results in a disconnected or trivial graph. In this paper we find an upper bound for the sum of the double domination number and connectivity of a graph and characterize the corresponding extremal graphs.