Skew spectrum and oriented graphs with same skew energy
Hilal A. Ganie, Rezwan Ul Shaban
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Source: Crossref
Published: Oct 7, 2025
DOI: 10.1142/s1793830925501307
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Let [Formula: see text] be an oriented graph with [Formula: see text] vertices and [Formula: see text] arcs having underlying graph [Formula: see text]. The skew matrix of [Formula: see text] denoted by [Formula: see text] is a [Formula: see text]-skew symmetric matrix. The skew eigenvalues of [Formula: see text] are the eigenvalues of [Formula: see text] and its characteristic polynomial is the skew characteristic polynomial of [Formula: see text]. The sum of the absolute values of the skew eigenvalues is the skew energy of [Formula: see text] and is denoted by [Formula: see text]. In this paper, we study the skew characteristic polynomial, skew eigenvalues of joined union of mixture of oriented bipartite graphs and Eulerian oriented graphs. As a special case we obtain the skew eigenvalues of join of a bipartite oriented graph and the Eulerian oriented graph. Some examples of orientations of well-known graphs are presented to highlight the importance of the results. As applications to our result, we obtain some new infinite families of skew equienergetic oriented graphs. Our results extend and generalize some of the results obtained in C. Adiga and B. R. Rakshith, More skew-equienergetic digraphs, Commun. Comb. Optim. 1(1) (2016) 55–71.
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