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Let S(Gσ) be the skew-adjacency matrix of an oriented graph Gσ with n vertices, and let λ1,λ2,…,λn be all eigenvalues of S(Gσ). The skew-spectral radius ρs(Gσ) of Gσ is defined as max{|λ1|,|λ2|,…,|λn|}. A connected graph, in which the number of edges equals the number of vertices, is called a unicyclic graph. In this paper, the structure of oriented unicyclic graphs whose skew-spectral radius does not exceed 2 is investigated. We order all the oriented unicyclic graphs with n vertices whose skew-spectral radius is bounded by 2.

Ordering the oriented unicyclic graphs whose skew-spectral radius is bounded by 2