Outdegree equitable domination number of certain graph operators

Abstract

For a vertex u in the dominating set D of a graph G, the number of edges from u to V-D is called the outdegree of u with respect to D, d°D, G(u). A dominating set D is called the outdegree equitable dominating set if the absolute value of the differences of outdegrees of any two vertices in D is at most one. The minimum cardinality of an outdegree equitable dominating set of G is called the outdegree equitable domination number of G, γoe(G). In this paper, we study the outdegree equitable domination number of certain graph operators such as complement, double graph, mycielskian and subdivision of graph.