Oriented unicyclic graphs with the first largest skew energies

Let Gσ be an oriented graph obtained by assigning an orientation σ to the edge set of a simple undirected graph G such that Gσ becomes a directed graph. Let S(Gσ) be the skew adjacency matrix of Gσ. The skew energy of Gσ is defined as the sum of the absolute values of all eigenvalues of S(Gσ). In this paper, we provide a new method to compare the skew energies of two oriented graphs whose skew characteristic polynomials satisfy a given recurrence relation and determine the oriented unicyclic graphs of order n with the first largest skew energies for n⩾31.