An infinite family of biquasiprimitive 2-arc transitive cubic graphs

TL;DR

This paper constructs and analyzes a new infinite family of bipartite cubic graphs that are highly symmetric, specifically 3-arc transitive, with unique automorphism properties not seen in previous examples.

Contribution

It introduces the first known infinite family of bipartite cubic 3-arc transitive graphs with a 2-arc transitive automorphism group exhibiting non-quasiprimitive behavior on bipartite halves.

Findings

First examples with a 2-arc transitive vertex-biquasiprimitive automorphism group

Automorphism group acts in a novel non-quasiprimitive way

Provides an infinite family of graphs with unique symmetry properties

Abstract

A new infinite family of bipartite cubic 3-arc transitive graphs is constructed and studied. They provide the first known examples admitting a 2-arc transitive vertex-biquasiprimitive group of automorphisms for which the index two subgroup fixing each half of the bipartition is not quasiprimitive on either bipartite half.