A new infinite family of star normal quotient graphs of twisted wreath type

TL;DR

This paper introduces infinite families of locally arc transitive graphs with specific automorphism group properties, expanding the classification of such graphs within the twisted wreath category.

Contribution

It constructs the first infinite families of graphs with the described automorphism group properties in the twisted wreath category.

Findings

First infinite families of such graphs constructed

Automorphism groups have two orbits on vertices

Group is quasiprimitive on exactly one orbit

Abstract

We construct the first infinite families of locally arc transitive graphs with the property that the automorphism group has two orbits on vertices and is quasiprimitive on exactly one orbit, of twisted wreath type. This work contributes to Giudici, Li and Praeger's program for the classification of locally arc transitive graphs by showing that the star normal quotient twisted wreath category also contains infinitely many graphs.