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An oriented graph  is a digraph without loops or multiple arcs whose underlying graph is . Let  be the skew-adjacency matrix of  and  be the independence number of . The rank of  is called the skew-rank of , denoted by . Wong et al. (Eur J Comb 54:76–86, ) studied the relationship between the skew-rank of an oriented graph and the rank of its underlying graph. In this paper, the correlation involving the skew-rank, the independence number, and some other parameters are considered. First we show that , where  is the order of  and () is the dimension of cycle space of . We also obtain sharp lower bounds for ,  and characterize all corresponding extremal graphs.

Relation between the skew-rank of an oriented graph and the independence number of its underlying graph