Volume :5 , Issue :4 ,Page :98-110

Abstract : For any graph G, let V(G) and E(G) denote the vertex set and edge set of G respectively. The Boolean function graph ) K , INC , K ( B q p of G is a graph with vertex set V(G)  E(G) and two vertices in ) K , INC , K ( B q p are adjacent if and only if they co rrespond to two adjac ent vertices of G, two nonadjacent vertices of G or to a vertex and an edge incident to it in G, For brevity, this graph is denoted by ) ( 4 G B . In this paper, structural properties of ) ( 4 G B including traversability and eccentricity properties are stud ied. Further, decomposition of ) G ( B 4 for some known graphs are given.