Tetravalent vertex-transitive graphs of order $6p$

TL;DR

This paper classifies tetravalent vertex-transitive graphs of order 6p, where p is prime, focusing on those that are not Cayley graphs, thereby advancing understanding of symmetric graph structures.

Contribution

It provides a complete classification of non-Cayley tetravalent vertex-transitive graphs of order 6p for all primes p, filling a gap in the graph theory literature.

Findings

Classification of non-Cayley graphs of order 6p

Identification of conditions for vertex-transitivity

Extension of known results to new graph orders

Abstract

A graph is vertex-transitive if its automorphism group acts transitively on vertices of the graph. A vertex-transitive graph is a Cayley graph if its automorphism group contains a subgroup acting regularly on its vertices. In this paper, the tetravalent vertex-transitive non-Cayley graphs of order $6p$ are classified for each prime $p$.