
TL;DR
This paper provides a comprehensive classification and explicit descriptions of all planar cubic Cayley graphs, revealing their structure, counterexamples to existing conjectures, and supporting computational analysis.
Contribution
It offers a complete description, explicit presentations, and embeddings for all planar cubic Cayley graphs, including new counterexamples and computational insights.
Findings
Complete classification of planar cubic Cayley graphs
Counterexamples to Mohar, Bonnington, and Watkins conjectures
Supports Droms' conjecture through computational analysis
Abstract
We obtain a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. We obtain counterexamples to conjectures of Mohar, Bonnington and Watkins. Our analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
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