3,548 research outputs found

    The skew energy of random oriented graphs

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    Given a graph GG, let GσG^\sigma be an oriented graph of GG with the orientation σ\sigma and skew-adjacency matrix S(Gσ)S(G^\sigma). The skew energy of the oriented graph GσG^\sigma, denoted by ES(Gσ)\mathcal{E}_S(G^\sigma), is defined as the sum of the absolute values of all the eigenvalues of S(Gσ)S(G^\sigma). In this paper, we study the skew energy of random oriented graphs and formulate an exact estimate of the skew energy for almost all oriented graphs by generalizing Wigner's semicircle law. Moreover, we consider the skew energy of random regular oriented graphs Gn,dσG_{n,d}^\sigma, and get an exact estimate of the skew energy for almost all regular oriented graphs.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1011.6646 by other author

    A characterization of skew Hadamard matrices and doubly regular tournaments

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    We give a new characterization of skew Hadamard matrices of size nn in terms of the data of the spectra of tournaments of size nβˆ’2n-2.Comment: 9 page
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