5-regular oriented graphs with optimum skew energy

Let $G$ be a simple undirected graph and $G^σ$ be the corresponding oriented graph of $G$ with the orientation $σ$. The skew energy of $G^σ$, denoted by $\varepsilon_s(G^σ)$, is defined as the sum of the singular values of the skew adjacency matrix $S(G^σ)$. In 2010, Adiga et al. certified that $\varepsilon_s(G^σ) \leq n\sqrtΔ$, where $Δ$ 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.

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