Restrained Edge Detour Domination of Network Graphs

Abstract

Let G be a connected graph with atleast two vertices. An edge detour dominating set S of V is called a restrained edge detour dominating set of a graph if for every vertex not in S is adjacent to a vertex in S and to a vertex in V- S. The minimum cardinality of such a dominating set is called a restrained edge detour domination number of G and is denoted by . In this paper, we have determined the restrained edge detour domination number for mesh network, torus network, Hexagonal network, Honeycomb network and its properties are studied.