skew equienergetic digraphs
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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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Journal title:
transactions on combinatoricsPublisher: university of isfahan
ISSN 2251-8657
volume 5
issue 1 2016
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