On Factor-Invariant Graphs With Two Cycles

TL;DR

This paper classifies a specific class of symmetric graphs with two cycles and an invariant 1-factor, expanding understanding of their structure and symmetry properties.

Contribution

It provides a complete classification of trivalent vertex-transitive graphs with a 2-factor of two cycles and an automorphism-invariant 1-factor.

Findings

Identifies all such graphs with the specified properties.

Characterizes the automorphism groups of these graphs.

Establishes conditions for the existence of these graphs.

Abstract

We classify trivalent vertex-transitive graphs whose edge sets have a partition into a 2-factor composed of two cycles and a 1-factor that is invariant under the action of the automorphism group.