Biequivalent Planar Graphs

Piette, Bernard

Abstract

We define biequivalent planar graphs, which are a generalisation of the uniform polyhedron graphs, as planar graphs made out of two families of equivalent nodes. Such graphs are required to identify polyhedral cages with geometries suitable for artificial protein cages. We use an algebraic method, which is followed by an algorithmic method, to determine all such graphs with up to 300 nodes each with valencies ranging between three and six. We also present a graphic representation of every graph found.

Citation

Piette, B. (2024). Biequivalent Planar Graphs. Axioms, 13(7), Article 437. https://doi.org/10.3390/axioms13070437

• Journal Article Type: Article
• Acceptance Date: Jun 24, 2024
• Online Publication Date: Jun 28, 2024
• Publication Date: 2024-07
• Deposit Date: Jul 25, 2024
• Publicly Available Date: Jul 25, 2024
• Journal: Axioms
• Electronic ISSN: 2075-1680
• Publisher: MDPI
• Peer Reviewed: Peer Reviewed
• Volume: 13
• Issue: 7
• Article Number: 437
• DOI: https://doi.org/10.3390/axioms13070437
• Keywords: Cayley graphs, polyhedral cages, uniform polyhedron, protein cage, 00A69, planar graphs, regular solids
• Public URL: https://durham-repository.worktribe.com/output/2529045