The oriented bicyclic graphs whose skew-spectral radii do not exceed 2

被引:0
作者
Guang-Hui Xu
Shi-Cai Gong
机构
[1] Zhejiang A & F University,School of Science
来源
Journal of Inequalities and Applications | / 2015卷
关键词
oriented graph; skew-adjacency matrix; skew-spectral radius; 05C20; 05C50; 15A18; 15C35;
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摘要
Let S(Gσ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S(G^{\sigma})$\end{document} be the skew-adjacency matrix of the oriented graph Gσ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$G^{\sigma}$\end{document} on order n and λ1,λ2,…,λn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lambda _{1},\lambda _{2},\ldots, \lambda _{n}$\end{document} be all eigenvalues of S(Gσ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S(G^{\sigma})$\end{document}. The skew-spectral radius ρs(Gσ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\rho_{s}(G^{\sigma})$\end{document} of Gσ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$G^{\sigma}$\end{document} is defined as max{|λ1|,|λ2|,…,|λn|}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\max\{|\lambda _{1}|,|\lambda _{2}|,\ldots,|\lambda _{n}|\}$\end{document}. In this paper, we determine all the oriented bicyclic graphs whose skew-spectral radii do not exceed 2.
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