Bicyclic oriented graphs with the second largest skew-energy

Let GσGσ be an oriented graph and Ps(Gσ;x)=det(xI−S(Gσ))Ps(Gσ;x)=det(xI−S(Gσ)) be the skew-characteristic polynomial of its skew-adjacency matrix S(Gσ)S(Gσ). The skew-energy of GσGσ is defined to be the sum of the absolute values of eigenvalues of S(Gσ)S(Gσ). In this paper, we firstly find a novel relation between the coefficients of skew-characteristic polynomial of unicyclic graph with the third largest skew-energy and bicyclic oriented graphs, and then use it along with other techniques to characterize the bicyclic oriented graphs with the second largest skew-energy.