Biequivalent Planar Graphs

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.

Keywords

• planar graphs
• Cayley graphs
• uniform polyhedron
• regular solids
• polyhedral cages
• protein cage