Volume :8 , Issue :4 ,Page :233 - 247

Abstract :For any simple graph G, let V(G) and E(G) denote the vertex set and edge set of G respectively. The Boolean function graph B( G, Kq, NINC ) of G is a graph with vertex set V(G) ? E(G) and two vertices in B(G, K , INC) q are adjacent if and only if they correspond to two nonadjacent vertices of G or to a vertex and an edge incident to it in G. For simplicity, this graph is denoted by BF1(G). Two vertices in the complement BF (G) 1 of BF1(G) are adjacent if and only if they correspond to two adjacent vertices of G, two adjacent edges of G, two nonadjacent edges of G or to a vertex and an edge not incident to it in G. In this paper, structural properties of the complement BF (G) 1 of BF1(G) including traversability and eccentricity properties are studied. Also covering numbers and various domination numbers are determined.