Further Results on Dual Domination in Graphs

Abstract

Let G = (V, E) be a simple graph. A set S V(G) is a dual dominating set of G (or bi-dominating set of G) if S is a dominating set of G and every vertex in S dominates exactly two vertices in V-S. The dual-domination number γdu(G) (or bi-domination number G bi  ) of a graph G is the minimum cardinality of the minimal dual dominating set (or dual dominating set). In this paper dual domination number and relation with other graph parameters are determined.