Skew-rank of an oriented graph with edge-disjoint cycles

An oriented graph [GRAPHICS] is a digraph without loops and multiple arcs, where [GRAPHICS] is called the underlying graph of [GRAPHICS] . Let [GRAPHICS] denote the skew-adjacency matrix of [GRAPHICS] . The rank of [GRAPHICS] is called the skew-rank of [GRAPHICS] , denoted by [GRAPHICS] , which is even since [GRAPHICS] is skew symmetric. Recently, Qu and Yu proved that [GRAPHICS] for an oriented bicyclic graph [GRAPHICS] with pendant vertices and with two edge-disjoint cycles of size [GRAPHICS] and [GRAPHICS] . In this paper, we extend this result to a more general case. It is proved that [GRAPHICS] if [GRAPHICS] is a connected oriented graph with [GRAPHICS] pairwise edge-disjoint cycles of size [GRAPHICS] . Moreover, the extremal graphs [GRAPHICS] attaining the lower bound are characterized.