Skew-rank of an oriented graph in terms of the rank and dimension of cycle space of its underlying graph

Yong Lu, Ligong Wang, Qiannan Zhou

Let $G^{\sigma }$ be an oriented graph and $S(G^{\sigma })$ be its skew-adjacency matrix, where $G$ is called the underlying graph of $G^{\sigma }$. The skew-rank of $G^{\sigma }$, denoted by $sr(G^{\sigma })$, is the ra…