VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • On tetravalent half-arc-transitive graphs of girth 5
    Antončič, Iva, 1986- ; Šparl, Primož
    A subgroup of the automorphism group of a graph is said to be half-arc-transitive on ▫$\Gamma$▫ if its action on ▫$\Gamma$▫ is transitive on the vertex set of ▫$\Gamma$▫ and on the edge set of ... ▫$\Gamma$▫ but not on the arc set of ▫$\Gamma$▫. Tetravalent graphs of girths ▫$3$▫ and ▫$4$▫ admitting a half-arc-transitive group of automorphisms have previously been characterized. In this paper we study the examples of girth ▫$5$▫. We show that, with two exceptions, all such graphs only have directed ▫$5$▫-cycles with respect to the corresponding induced orientation of the edges. Moreover, we analyze the examples with directed ▫$5$▫-cycles, study some of their graph theoretic properties and prove that the ▫$5$▫-cycles of such graphs are always consistent cycles for the given half-arc-transitive group. We also provide infinite families of examples, classify the tetravalent graphs of girth ▫$5$▫ admitting a half-arc-transitive group of automorphisms relative to which they are tightly-attached and classify the tetravalent half-arc-transitive weak metacirculants of girth ▫$5$▫.
    Vir: Discrete mathematics. - ISSN 0012-365X (Vol. 346, iss. 10, art. 113577, 2023, str. 1-17)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2023
    Jezik - angleški
    COBISS.SI-ID - 157544707

    Povezava(-e):

    https://www.sciencedirect.com/science/article/pii/S0012365X23002637?via%3Dihub
    https://doi.org/10.1016/j.disc.2023.113577
    DOI

vir: Discrete mathematics. - ISSN 0012-365X (Vol. 346, iss. 10, art. 113577, 2023, str. 1-17)
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