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  • Median eigenvalues of bipartite graphs
    Mohar, Bojan, 1956- ; Tayfeh-Rezaie, Behruz, 1971-
    For a graph ▫$G$▫ of order ▫$n$▫ and with eigenvalues ▫$\lambda_1 \geqslant \cdots \geqslant \lambda_n$▫, the HL-index ▫$R(G)$▫ is defined as ▫$R(G) = {\max} \left\{ ... |\lambda_{\lfloor(n+1)/2\rfloor}|, |\lambda_{\lceil(n+1)/2\rceil}| \right\}$▫. We show that for every connected bipartite graph ▫$G$▫ with maximum degree ▫$\Delta \geqslant 3$▫, ▫$R(G) \leqslant \sqrt{\Delta-2}$▫ unless ▫$G$▫ is the the incidence graph of a projective plane of order ▫$\Delta-1$▫. We also present an approach through graph covering to construct infinite families of bipartite graphs with large HL-index.
    Vir: Journal of algebraic combinatorics. - ISSN 0925-9899 (Vol. 41, iss. 3, 2015, str. 899-909)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2015
    Jezik - angleški
    COBISS.SI-ID - 17633113

    Povezava(-e):

    http://dx.doi.org/10.1007/s10801-014-0558-x

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