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An oriented graph Gσ is a digraph without loops and multiple arcs, where G is the underlying graph of Gσ. Let S(Gσ) denote the skew-adjacency matrix of Gσ, and A(G) be the adjacency matrix of G. The rank (resp. skew-rank) of G (resp. Gσ), written as r(G) (resp. sr(Gσ)), refers to the rank of A(G) (resp. S(Gσ)). It is natural and interesting to study the relationship between sr(Gσ) and r(G). Wong,...
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