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

n oriented graph G^σ is a digraph without loops or multiple arcs whose underlying graph is G . Let S( G^σ) be the skew-adjacency matrix of G^σ and α (G) be the independence number of G . The rank of S(G^σ ) is called the skew-rank of G^σ , denoted by sr(G^σ ) . Wong et al. (Eur J Comb 54:76–86, 2016 ) 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 sr(G^σ )+2α (G)⩾ 2|V_G|-2d(G) , where |V_G| is the order of G and d ( G ) is the dimension of cycle space of G . We also obtain sharp lower bounds for sr(G^σ )+α (G), sr(G^σ )-α (G) , sr(G^σ )/α (G) and characterize all corresponding extremal graphs.