Geodesic
A classification of pentavalent arc-transitive bicirculants
Journal of Algebraic Combinatorics, Tome 41 (2015) no. 3, pp. 643-668.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 $\mathrm{Cay}(D_{2n},\{b,ba,ba^{r+1},ba^{r^2+r+1},ba^{r^3+r^2+r+1}\})$ on the dihedral group $D_{2n}=\langle a,b\mid a^n=b^2=baba=1\rangle$, where $r\in\mathbb Z_n^*$ such that $r^4+r^3+r^2+r+1\equiv 0\pmod{n}$.
Classification : 05C25, 05C85, 05C12, 05C60, 05C38
Keywords: vertex-transitive, edge-transitive, arc-transitive 
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     title = {A classification of pentavalent arc-transitive bicirculants},
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Antončič, Iva; Hujdurović, Ademir; Kutnar, Klavdija. A classification of pentavalent arc-transitive bicirculants. Journal of Algebraic Combinatorics, Tome 41 (2015) no. 3, pp. 643-668. http://geodesic.mathdoc.fr/item/JAC_2015__41_3_a10/