Skew equienergetic digraphs

Let D D be a digraph with skew-adjacency matrix S(D) S(D) ‎. ‎The skew‎ ‎energy of D D is defined as the sum of the norms of all‎ ‎eigenvalues of S(D) S(D) ‎. ‎Two digraphs are said to be skew‎ ‎equienergetic if their skew energies are equal‎. ‎We establish an‎ ‎expression for the characteristic polynomial of the skew‎ ‎adjacency matrix of the join of two digraphs‎, ‎and for the‎ ‎respective skew energy‎, ‎and thereby construct non cospectral‎, ‎skew equienergetic digraphs on n n vertices‎, ‎for all n≥6 n≥6‎. ‎Thus we arrive at the solution of some open problems proposed in‎ ‎[X‎. ‎Li‎, ‎H‎. ‎Lian‎, ‎A survey on the skew energy of oriented graphs‎, ‎arXiv:1304.5707]‎.