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The Planar Cubic Cayley Graphs

About this Title

Agelos Georgakopoulos

Publication: Memoirs of the American Mathematical Society
Publication Year: 2017; Volume 250, Number 1190
ISBNs: 978-1-4704-2644-6 (print); 978-1-4704-4204-0 (online)
Published electronically: September 7, 2017
Keywords:Cayley graph, planar graph, planar presentation, amalgamation

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Table of Contents


  • Chapter 1. Introductory material and basic facts
  • Chapter 2. The finite and 1-ended cubic planar Cayley graphs
  • Chapter 3. The planar multi-ended Cayley graphs with 2 generators
  • Chapter 4. The planar multi-ended Cayley graphs generated by 3 involutions
  • Chapter 5. Outlook


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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