Minimal skew energy of oriented unicyclic graphs with a perfect matching.

Let G^σ be an oriented graph of a simple undirected graph G with an orientation σ, which assigns to each edge of G a direction so that the resultant graph G^σ becomes a directed graph. The skew energy of G^σ is defined as the sum of the absolute values of all eigenvalues of the skew-adjacency matrix of G^σ. Denote by U^σ (2k) the set of all oriented unicyclic graphs on 2k vertices with a perfect matching which contain no cycle of length l with l ≡ 2(mod 4). In this paper, we characterize the oriented graphs of U^σ (2k) with the minimal skew energy for k ≥ 4. [ABSTRACT FROM AUTHOR]