Cubic vertex-transitive graphs admitting automorphisms of large orderPotočnik, Primož (Avtor) Toledo, Micael (Avtor) cubic vertex-transitive graphsmulticirculantsautomorphisms of large orderA connected graph of order $n$ admitting a semiregular automorphism of order $n/k$ is called a $k$-multicirculant. Highly symmetric multicirculants of small valency have been extensively studied, and several classification results exist for cubic vertex- and arc-transitive multicirculants. In this paper, we study the broader class of cubic vertex-transitive graphs of order $n$ admitting an automorphism of order $n/3$ or larger that may not be semiregular. In particular, we show that any such graph is either a $k$-multicirculant for some $k \le 3$, or it belongs to an infinite family of graphs of girth $6$.20232024-03-18 08:52:19Neznano18433sl