Volume :5 , Issue :1 ,Page :1-23
Abstract :Let G be a simple (p, q) graph with vertex set V(G) and edge set E(G). B G, INC, L(G) (G) is a graph with vertex set V(G) E(G) and two vertices are adjacent if and only if they correspond to two adjacent vertices of G, to a vertex and an edge incident to it in G or two non-adjacent edges of G. For simplicity, denote this graph by BG 2 (G), Boolean graph of G-second kind. Similarly, B K p , INC, L(G)(G) is a graph with the same vertex set and two vertices are adjacent if and only if they correspond to a vertex and an edge incident to it in G or two non-adj acent edges of G. For simplicity, denote this graph by BG 3 (G), Boolean graph of G-third kind. In this paper, characterizations of BG 2 (G), BG 3 (G) and partitions of edges of BG 2 (G), BG 3 (G) and their complements are studied.