Symmetry Group of (3,6)-Fullerenes

Abstract

A (3,6)-fullerene is a 3-connected cubic planar graph whose faces are triangles and hexagons. In this paper, it is proved that for a (3,6)-fullerene graph F, |Aut(F)| divides 24. An open question is also presented.

Keywords:

• fullerenes
• group action
• stabilizer
• automorphism group

Acknowledgments

The authors are very grateful to referee(s) for suggestions and helpful remarks. We are indebted to Professor Patrick W. Fowler for the critical discussion of this paper. We are also indebted to F. Koorepazan-Moftakhar for her help in computing symmetry group of some (3,6)-fullerenes.

Funding

The research of the third author is partially supported by the University of Kashan under grant No. 159020/48.