Bicyclic oriented graphs with skew-rank 2 or 4

The skew-rank of oriented graph GσGσ, denoted by sr(Gσ)sr(Gσ), is the rank of the skew-adjacency matrix of GσGσ. The skew-rank is even since the skew-adjacency matrix is skew-symmetric. In this paper we characterize the bicyclic oriented graphs with skew-rank 2 or 4.