Degree Equal Dominating Set of a Graph

A subset D of V is called dominating set if for any vertex u in V-D, there exist at least one vertex v in D such that u and v are adjacent. A subset D of a graph G is called a degree equal dominating set of G if for any u in V-D, there exists v in D such that u and v are adjacent and deg(u) = deg(v). In a social network, members who are neighbors and who have equal status can dominate each other. In the sense, the domination is symmetric. A graph model for this network leads to the concept of degree equal domination. In this paper we define and study the degree equal dominating set of a graph, degree equal irredundant sets in a graph, independent degree equal dominating set of a graph, degree equal complete graphs, 2-equal packing number of a graph.