Semiregular automorphisms of cubic vertex-transitive graphs

TL;DR

This paper characterizes certain symmetric properties of cubic graphs with vertex-transitive automorphism groups, showing how the size of semiregular subgroups relates to the graph's order.

Contribution

It provides a new characterization of cubic graphs with specific automorphism group structures and demonstrates how the size of semiregular subgroups scales with the graph's order.

Findings

Connected cubic graphs with specific automorphism groups are characterized.

The size of maximum semiregular subgroups grows with the graph's order.

Abstract

We characterise connected cubic graphs admitting a vertex- transitive group of automorphisms with an abelian normal subgroup that is not semiregular. We illustrate the utility of this result by using it to prove that the order of a semiregular subgroup of maximum order in a vertex-transitive group of automorphisms of a connected cubic graph grows with the order of the graph.