A graph Γ is said to be an m-Cayley graph on a group G (|G| ≠ 1) if its automorphism group contains a semiregular subgroup isomorphic to G having m orbits on the vertex set of Γ. If G is cyclic and m = 3 then Γ is called a tricirculant. A graph is said to be symmetric if its automorphism group acts transitively on the set of its arcs. In this paper, it is shown that with the exception of K₆, no connected pentavalent symmetric tricirculant exists.
Khaefi et al. (Fri,) studied this question.