Skew equienergetic digraphs

Document Type: Research Paper

Authors

1 Karnatak University, Dharwad, India

2 Karnatak University, Dharwad

3 University of Kragujevac, 34000 Kragujevac

4 Nankai University, Tianjin

Abstract

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]‎.
 

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