Note on skew-eigenvalues of digraphs

Taghvaee, Fatemeh; Fath-Tabar, Gholam Hossein

doi:10.22108/toc.2023.134342.2001

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	Note on skew-eigenvalues of digraphs
Transactions on Combinatorics
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نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2023.134342.2001
نویسندگان
Fatemeh Taghvaee^* ؛ Gholam Hossein Fath-Tabar
Department of Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran
چکیده
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.
کلیدواژه‌ها
Skew adjacency matrix؛ Oriented graph؛ Skew-eigenvalue

مراجع
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Note on skew-eigenvalues of digraphs