Bicyclic oriented graphs with skew-rank 6

Let Gσ be an oriented graph and S(Gσ) be its skew-adjacency matrix. The skew-rank of Gσ, denoted by sr(Gσ), is the rank of S(Gσ). In this paper, we characterize all the bicyclic oriented graphs with skew-rank 6. Let Gσ   be a bicyclic oriented graph with pendant vertices but no pendant twins. If sr(Gσ)=6,sr(Gσ)=6, then 6 ≤ |V(Gσ)| ≤ 10.