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Cubic vertex-transitive graphs admitting automorphisms of large orderPrimož Potočnik,
Micael Toledo, 2023, original scientific article
Abstract: A 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 $6$.
Keywords: cubic vertex-transitive graphs, multicirculants, automorphisms of large order
Published in DiRROS: 18.03.2024; Views: 92; Downloads: 50
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