A Survey on Symmetry Group of Polyhedral Graphs

Abstract

Every three-connected simple planar graph is a polyhedral graph and a cubic polyhedral graph with pentagonal and hexagonal faces is called as a classical fullerene. The aim of this paper is to survey some results about the symmetry group of cubic polyhedral graphs. We show that the order of symmetry group of such graphs divides 240.

Keywords

• polyhedral graph
• fullerene
• automorphism group
• group action