Volume :6 , Issue :1 ,Page :1-16

Abstract : Let G be a simple (p, q) graph with vertex set V(G) and edge set E(G). B G, NINC,  Kq (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 or to a vertex and an edge not in cident to it in G. For simplicity, denote this graph by BG 1 (G), Boolean graph of G-first kind. In this paper, some properties of BG 1 (G) including eccentricity properties and covering numbers are studied.