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  • On the number of closed walks in vertex-transitive graphs
    Jajcay, Robert ; Malnič, Aleksander ; Marušič, Dragan
    The results of Širáň and the first author [A construction of vertex-transitive non-Cayley graphs, Australas. J. Combin. 10 (1994) 105-114; More constructions of vertex-transitive non-Cayley graphs ... based on counting closed walks, Australas. J. Combin. 14 (1996) 121-132] are generalized, and new formulas for the number of closed walks of length ▫$p^r$▫ or ▫$pq$▫, where ▫$p$▫ and ▫$q$▫ are primes, valid for all vertex-transitive graphs are found. Based on these formulas, several simple tests for vertex-transitivity are presented, as well as lower bounds on the orders of the smallest vertex- and arc-transitive groups of automorphisms for vertex-transitive graphs of given valence.
    Vir: Discrete mathematics. - ISSN 0012-365X (Vol. 307, iss. 3-5, 2007, str. 484-493)
    Vrsta gradiva - članek, sestavni del
    Leto - 2007
    Jezik - angleški
    COBISS.SI-ID - 14181209

vir: Discrete mathematics. - ISSN 0012-365X (Vol. 307, iss. 3-5, 2007, str. 484-493)

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