Note on skew-eigenvalues of digraphs

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran

Abstract

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.

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Main Subjects


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Volume 13, Issue 3 - Serial Number 3
September 2024
Pages 225-234
  • Receive Date: 12 July 2022
  • Revise Date: 06 June 2023
  • Accept Date: 08 June 2023
  • Published Online: 01 September 2024