Let G be a graph with V(G) = {nu(1),..., nu(n)} and E(G) = {e(1),..., e(m)). In this paper, only graphs with no multiple edges are observed. The n x n matrix A = [a(ij)], where a(ij) = 1 if e = nu(i)nu(j) epsilon E(G) and a(ij) = 0 otherwise, is the adjacency matrix of G and is denoted by A(G). The n x n matrix B = [b(ij)], where b(ij) = 0 if e = nu(i)nu(j) epsilon E(G) and b(ij) = 1 otherwise, is the antiadjacency matrix of G and is denoted by B (G). Boolean operations on two graphs have been examined by Harary and Wilcox. Hence, this paper will consider Boolean operations on two adjancency and antiadjancency matrices of two graphs G(1) and G(2) with V(G(1)) = V(G(2)). Boolean operations which are reviewed on this paper are OR (V), AND (A), XOR(circle plus), and NXOR((circle plus) over bar) However, the paper only focus on operation circle plus and (circle plus) over bar. The purposes of this paper are to introduce the operations on two adjacency and antiadjacency matrices of two graphs G(1) and G(2) with V(G(1)) = V(G(2)), to reveal the effect on the represented graph using operations circle plus and (circle plus) over bar on both adjacency and antiadjacency matrices, and to compare the largest eigenvalues between the matrices generated by the Boolean operations.
