Tetravalent s-transitive graphs of order $6p^2$

TL;DR

This paper classifies all tetravalent s-transitive graphs of order 6p^2, exploring their automorphism groups and symmetry properties for various values of p.

Contribution

It provides a complete classification of tetravalent s-transitive graphs of order 6p^2, detailing their automorphism groups and symmetry levels.

Findings

Classification of all such graphs for various primes p

Identification of automorphism group structures

Insights into symmetry properties of these graphs

Abstract

Let $s$ be a positive integer. A graph is $s$-transitive if its automorphism group is transitive on s-arcs but not on $(s + 1)$-arcs. In this paper, we study all tetravalent s-transitive graphs of order $6p^2$.