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  • Half-arc-transitive graphs of order ▫$4p$▫ of valency twice a prime
    Wang, Xiuyun ; Feng, Yan-Quan
    A graph is half-arc-transitive if its automorphism group acts transitively on vertices and edges, but not on arcs. Let ▫$p$▫ be a prime. Cheng and Oxley [On weakly symmetric graphs of order twice a ... prime, J. Combin. Theory B 42 (1987),196-211] proved that there is no half-arc-transitive graph of order ▫$2p$▫, and Alspach and Xu [1/2-transitive graphs of order ▫$3p$▫, J. Algebraic Combin. 3 (1994), 347-355] classified half-arc-transitive graphs of order ▫$3p$▫. In this paper we classify half-arc-transitive graphs of order ▫$4p$▫ of valency ▫$2q$▫ for each prime ▫$q \ge 5$▫. It is shown that such graphs exist if and only if ▫$p - 1$▫ is divisible by ▫$4q$▫. Moreover, for such ▫$p$▫ and ▫$q$▫ a unique half-arc-transitive graph of order ▫$4p$▫ and valency ▫$2q$▫ exists and this graph is a Cayley graph.
    Vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 3, no. 2, 2010, str. 151-163)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2010
    Jezik - angleški
    COBISS.SI-ID - 15859033

    Povezava(-e):

    http://amc.imfm.si/index.php/amc/article/viewFile/125/111
    Digitalna knjižnica Slovenije - dLib.si

vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 3, no. 2, 2010, str. 151-163)

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