Skew-eigenvalues of Cartesian and lexicographic products of graphs

Abstract

Let G = (V,E) be a simple graph and let G^f be an oriented graph of G with the orientation f and skew-adjacency matrix S(G^f) . The spectrum of S(G^f) consisting of all the eigenvalues of S(G^f) is called the skew-spectrum of G^f and denoted by Sp(G^f). In this paper, we consider an orientation of the Cartesian product of G_1 and G _2 and also an orientation of the lexicographic product G_1[G_2] of G_1 and G_2 and then we determine their skew adjacency matrix.