Tetravalent half-arc-transitive graphs of order $12p$

TL;DR

This paper classifies all tetravalent half-arc-transitive graphs of order 12p, where p is a prime, expanding understanding of symmetric graph structures with specific automorphism properties.

Contribution

It provides a complete classification of tetravalent half-arc-transitive graphs of order 12p, a previously unexplored family of symmetric graphs.

Findings

Identified all such graphs for various primes p

Established structural properties of these graphs

Contributed to the theory of half-arc-transitive graphs

Abstract

A graph is half-arc-transitive if its automorphism group acts transitively on its vertex set, edge set, but not its arc set. In this paper, we study all tetravalent half-arc-transitive graphs of order $12p$.