Volume :3 , Issue :3 ,Page :142-151

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 B(  K p , NINC,  L(G)) of G is a graph with vertex set V(G)  E(G) and two vertices in B(  K p , NINC,  L(G)) are adjacent if and only if they correspond to two nonadjacent edges of G or to a vertex and an edge not incident to it in G, where L(G) is the line graph of G. For brevity, this graph is denoted by B 3 (G). In this paper, structural properties of B 3 (G) including traversability and eccentricity properties are studied. Also the graphs G for which B 3 (G) contains C n , for n  4 are obtained. Further, decomposition of B 3 (G) for some known graphs are given.