University of Isfahan Transactions on Combinatorics 2251-8657 5 1 2016 03 01 Skew equienergetic digraphs 15 23 9372 10.22108/toc.2016.9372 EN Harishchandra S. Ramane Karnatak University, Dharwad, India K. Channegowda Nandeesh Karnatak University, Dharwad Ivan Gutman University of Kragujevac, 34000 Kragujevac Xueliang Li Nankai University, Tianjin Journal Article 2014 12 19 Let $D$ be a digraph with skew-adjacency matrix $S(D)$‎. ‎The skew‎ ‎energy of $D$ is defined as the sum of the norms of all‎ ‎eigenvalues of $S(D)$‎. ‎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 $n$ vertices‎, ‎for all $n \geq 6$‎. ‎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]‎. <br />  https://toc.ui.ac.ir/article_9372_1d921f94d58d62e8f06d43db2dc426d5.pdf