Double Domination Number of Some Families of Graph

Abstract

In a graph G = (V, E) each vertex is said to dominate every vertex in its closed neighborhood. In a graph G, if S is a subset of V then S is a double dominating set of G if every vertex in V is dominated by at least two vertices in S. The smallest cardinality of a double dominating set is called the double domination number γx2 (G). [4]. In this paper, we computed some relations between double domination number, domination number, number of vertices (n) and maximum degree (Δ) of Helm graph, Friendship graph, Ladder graph, Circular Ladder graph, Barbell graph, Gear graph and Firecracker graph.