Note on skew-eigenvalues of digraphs

Let G^\sigma be an oriented graph with underlying simple graph G. The skew-adjacency matrix of G^\sigma is the \{۰, ۱, -۱\}-matrix S=S(G^\sigma)=[s_{ij}], such that s_{ij}=۱ if (v_i, v_j) is an arc in G^\sigma, s_{ij}=-۱ if (v_j, v_i) is an arc in G^\sigma and s_{ij}=۰, otherwise. In this paper, all connected oriented graphs with three distinct skew-eigenvalues ۰ and \pm ۲ \mathbf{i} are characterized.

کلیدواژه ها:

skew adjacency matrix ، oriented graph ، Skew-eigenvalue