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  • Generalized Gardiner-Praeger graphs and their symmetries
    Miklavič, Štefko ; Šparl, Primož ; Wilson, Steve, matematik
    A subgroup of the automorphism group of a graph acts half-arc-transitively on the graph if it acts transitively on the vertex-set and on the edge-set of the graph but not on the arc-set of the graph. ... If the full automorphism group of the graph acts half-arc-transitively, the graph is said to be half-arc-transitive. A. Gardiner and C. E. Praeger [Eur. J. Comb. 15, No. 4, 375--381 (1994)] introduced two families of tetravalent arc-transitive graphs, called the ▫$C^{\pm 1}$▫ and the ▫$C^{\pm \varepsilon}$▫ graphs, that play a prominent role in the characterization of the tetravalent graphs admitting an arc-transitive group of automorphisms with a normal elementary abelian subgroup such that the corresponding quotient graph is a cycle. All of the Gardiner-Praeger graphs are arc-transitive but admit a half-arc-transitive group of automorphisms. Quite recently,P. Potočnik and S. E. Wilson [Art Discrete Appl. Math. 3, No. 1, Paper No. P1.08, 33 p. (2020)] introduced the family of ▫$\operatorname{CPM}$▫ graphs, which are generalizations of the Gardiner-Praeger graphs. Most of these graphs are arc-transitive, but some of them are half-arc-transitive. In fact, at least up to order 1000, each tetravalent half-arc-transitive loosely-attached graph of odd radius having vertex-stabilizers of order greater than 2 is isomorphic to a ▫$\operatorname{CPM}$▫ graph. In this paper we determine the automorphism group of the ▫$\operatorname{CPM}$▫ graphs and investigate isomorphisms between them. Moreover, we determine which of these graphs are 2-arc-transitive, which are arc-transitive but not 2-arc-transitive, and which are half-arc-transitive.
    Vir: Discrete mathematics. - ISSN 0012-365X (Vol. 344, iss. 3, March 2021, art. 112263 (22 str.))
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2021
    Jezik - angleški
    COBISS.SI-ID - 43857411

    Povezava(-e):

    https://www.sciencedirect.com/science/article/abs/pii/S0012365X20304490
    Repozitorij Univerze na Primorskem - RUP
    DOI

vir: Discrete mathematics. - ISSN 0012-365X (Vol. 344, iss. 3, March 2021, art. 112263 (22 str.))
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