New skew equienergetic oriented graphs

Abstract

Let $S(G^{\sigma})$ be the skew-adjacency matrix of the oriented graph $G^{\sigma}$, which is obtained from a simple undirected graph $G$ by assigning an orientation $\sigma$ to each of its edges. The skew energy of an oriented graph $G^{\sigma}$ is defined as the sum of absolute values of all eigenvalues of $S(G^{\sigma})$. Two oriented graphs are said to be skew equienergetic if their skew energies are equal. In this paper, we determine the skew spectra of some new oriented graphs. As applications, we give some new methods to construct new non-cospectral skew equienergetic oriented graphs.

Keywords

• Oriented graph
• Skew energy