On the Skew Spectra of Cartesian Products of Graphs

An oriented graph G is a simple undirected graph G with an orientation σ, which assigns to each edge of G a direction so that G becomes a directed graph. G is called the underlying graph of G and we denote by S(G) the skew-adjacency matrix of G and its spectrum Sp(G) is called the skew-spectrum of G. In this paper, the skew spectra of two orientations of the Cartesian product of two graphs are discussed. As applications, new families of oriented bipartite graphs G with Sp(G) = iSp(G) are given and the orientation of a product graph with maximum skew energy is obtained. AMS Mathematics Subject Classification(2000): 05C20 05C50