Classification of pentavalent symmetric tricirculantsKhaefi, Yasamin (Avtor) Kutnar, Klavdija (Avtor) Marušič, Dragan (Avtor) pentavalent graphsymmetricsemiregular automorphismtricirculantA graph $\Gamma$ is said to be an {\em $m$-Cayley graph} on a group $G$ ($|G|\ne 1$) if its automorphism group contains a semiregular subgroup isomorphic to $G$ having $m$ orbits on the vertex set of $\Gamma$. If $G$ is cyclic and $m=3$ then $\Gamma$ is called a {\em tricirculant}. A graph is said to be {\em symmetric} if its automorphism group acts transitively on the set of its arcs. In this paper, it is shown that with the exception of $K_6$, no connected pentavalent symmetric tricirculant exists.20262026-06-22 08:35:11Članek v reviji23172sl