Boolean Graph Operator B

Let G be a simple (p, q) graph with vertex set V(G) and edge set E(G). B is a graph with vertex set V(G) ∪ E(G) and two vertices are adjacent if and only if they correspond to two non adjacent vertices of G, a vertex and an edge not incident to it in G. For simplicity, denote this graph by BG(G), Boolean graph of G. In this paper, some properties of BG(G) are studied.