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  • Quasi-▫$\lambda$▫-distance-balanced graphs
    Abedi, Amirabbas ...
    A graph ▫$G$▫ is said to be quasi-▫$\lambda$▫-distance-balanced if for every pair of adjacent vertices ▫$u$▫ and ▫$v$▫, the number of vertices that are closer to ▫$u$▫ than to ▫$v$▫ is ▫$\lambda$▫ ... times bigger (or ▫$\lambda$▫ times smaller) than the number of vertices that are closer to ▫$v$▫ than to ▫$u$▫, for some positive rational number ▫$\lambda > 1$▫. This paper introduces the concept of quasi-▫$\lambda$▫-distance-balanced graphs, and gives some interesting examples and constructions. It is proved that every quasi-▫$\lambda$▫-distance-balanced graph is triangle-free. It is also proved that the only quasi-▫$\lambda$▫-distance-balanced graphs of diameter two are complete bipartite graphs. In addition, quasi-▫$\lambda$▫-distance-balanced Cartesian and lexicographic products of graphs are characterized. Connections between symmetry properties of graphs and the metric property of being quasi-▫$\lambda$▫-distance-balanced are investigated. Several open problems are posed.
    Vir: Discrete applied mathematics. - ISSN 0166-218X (Vol. 227, 2017, str. 21-28)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2017
    Jezik - angleški
    COBISS.SI-ID - 18032985

    Povezava(-e):

    http://dx.doi.org/10.1016/j.dam.2017.04.030
    DOI

vir: Discrete applied mathematics. - ISSN 0166-218X (Vol. 227, 2017, str. 21-28)

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