University of Isfahan Transactions on Combinatorics 2251-8657 13 3 2024 09 01 Note on skew-eigenvalues of digraphs 225 234 27603 10.22108/toc.2023.134342.2001 EN Fatemeh Taghvaee Department of Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran Gholam Hossein Fath-Tabar Department of Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran Journal Article 2022 07 12 Let $G^\sigma$ be an oriented graph with underlying simple graph $G$. The skew-adjacency matrix of $G^\sigma$ is the $\{0, 1, -1\}$-matrix $S=S(G^\sigma)=[s_{ij}]$, such that $s_{ij}=1$ if $(v_i, v_j)$ is an arc in $G^\sigma$, $s_{ij}=-1$ if $(v_j, v_i)$ is an arc in $G^\sigma$ and $s_{ij}=0$, otherwise. In this paper, all connected oriented graphs with three distinct skew-eigenvalues $0$ and $\pm 2 \mathbf{i}$ are characterized. https://toc.ui.ac.ir/article_27603_cef3b48b74faba995328a9105e0f095f.pdf