On the skew spectra of Cartesian products of graphs
Summary: An oriented graph \({G^{\sigma}}\) is a simple undirected graph \(G\) with an orientation, which assigns to each edge of \(G\) a direction so that \({G^{\sigma}}\) becomes a directed graph. \(G\) is called the underlying graph of \({G^{\sigma}}\) and we denote by \(S({G^{\sigma}})\) the skew-adjacency matrix of \({G^{\sigma}}\) and its spectrum \(Sp({G^{\sigma}})\) is called the skew-spectrum of \({G^{\sigma}}\). In this paper, the skew spectra of two orientations of the Cartesian products are discussed, as applications, new families of oriented bipartite graphs \({G^{\sigma}}\) with \(Sp({G^{\sigma}})=\mathbf {i} Sp(G)\) are given and the orientation of a product graph with maximum skew energy is obtained.
scientific article; zbMATH DE number 6171934