On the skew energy of orientations of hypercubes

Let D be a digraph of order n and λ1,λ2,…,λn denote all the eigenvalues of the skew-adjacency matrix of D. The skew energy ES(D) of D is defined as . In this paper, it is proved that for any positive integer k≥3, there exists a k-regular graph of order n having an orientation D with . This work positively answers a problem proposed by Adiga et al. [C. Adiga, R. Balakrishnan, Wasin So, The skew energy of a digraph, Linear Algebra Appl. 432 (2010) 1825–1835]. In addition, a digraph is also constructed such that its skew energy is the same as the energy of its underlying graph.