Minimal skew energy of oriented unicyclic graphs with a perfect matching

Abstract

Let 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 becomes a directed graph. The skew energy of is defined as the sum of the absolute values of all eigenvalues of the skew-adjacency matrix of . Denote by the set of all oriented unicyclic graphs on 2k vertices with a perfect matching which contain no cycle of length l with . In this paper, we characterize the oriented graphs of with the minimal skew energy for . MSC:05C50, 15A30.