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  • On the Cayleyness of Praeger-Xu graphs
    Jajcay, Robert ; Potočnik, Primož, 1971- ; Wilson, Steve, matematik
    This paper discusses a family of graphs, called Praeger-Xu graphs and denoted ▫$\operatorname{PX}(n, k)$▫ here, introduced by C. E. Praeger and M. Xu [Eur. J. Comb. 10, No. 1, 91-102 (1989)]. These ... tetravalent graphs are distinguished by having large symmetry groups; their vertex-stabilizers can be arbitrarily larger than the number of vertices in the graph. This paper does the following: (1) exhibits a connection between vertex-transitive groups of symmetries in a Praeger-Xu graph and certain linear codes, (2) characterizes those linear codes, (3) characterizes Praeger-Xu graphs ▫$\operatorname{PX}(n, k)$▫ which are Cayley, (4) shows that every ▫$\operatorname{PX}(n, k)$▫ is quasi-Cayley, and (5) constructs an infinite family of Praeger-Xu graphs in which a smallest vertex-transitive group of symmetries has arbitrarily large vertex-stabiliser.
    Vir: Journal of combinatorial theory. Series B. - ISSN 0095-8956 (Vol. 152, Jan. 2022, str. 55-79)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2022
    Jezik - angleški
    COBISS.SI-ID - 89816835

    Povezava(-e):

    https://www.sciencedirect.com/science/article/pii/S0095895621000769
    DOI

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