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Antončič, Iva; Hujdurović, Ademir; Kutnar, Klavdija
Journal of algebraic combinatorics, 05/2015, Letnik: 41, Številka: 3Journal Article
A bicirculant is a graph admitting an automorphism with two cycles of equal length in its cycle decomposition. A graph is said to be arc-transitive if its automorphism group acts transitively on the set of its arcs. All cubic and tetravalent arc-transitive bicirculants are known, and this paper gives a complete classification of connected pentavalent arc-transitive bicirculants. In particular, it is shown that, with the exception of seven particular graphs, a connected pentavalent bicirculant is arc-transitive if and only if it is isomorphic to a Cayley graph Cay ( D 2 n , { b , b a , b a r + 1 , b a r 2 + r + 1 , b a r 3 + r 2 + r + 1 } ) on the dihedral group D 2 n = ⟨ a , b ∣ a n = b 2 = b a b a = 1 ⟩ , where r ∈ Z n ∗ such that r 4 + r 3 + r 2 + r + 1 ≡ 0 ( mod n ) .
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