5-regular oriented graphs with optimum skew energy

Abstract

Let $G$ be a simple undirected graph and $G^{\sigma }$ be the corresponding oriented graph of $G$ with the orientation $\sigma$. The skew energy of $G^{\sigma }$, denoted by ${\epsilon }_s(G^{\sigma })$, is defined as the sum of the singular values of the skew adjacency matrix $S(G^{\sigma })$. In 2010, Adiga et al. certified that ${\epsilon }_s(G^{\sigma })\le n\sqrt{\Delta }$, where $\Delta$ is the maximum degree of $G$ of order $n$. In this paper, we determine all connected 5-regular oriented graphs of order $n$ with maximum skew-energy.

27 Pages, 2 tables, 4 figures