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Abstract: A 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.
Keywords: pentavalent graph, symmetric, semiregular automorphism, tricirculant
Published in RUP: 22.06.2026; Views: 483; Downloads: 10
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