Enumeration formulas for (3, 6)-fullerenes
Abstract
A (3, 6)-fullerene is a cubic planar graph whose faces all have 3 or 6 sides. We give an exact enumeration of (3, 6)-fullerenes with V vertices. We also enumerate (3, 6)-fullerenes with mirror symmetry, with 3-fold rotational symmetry, and with both types of symmetry. The resulting formulas are expressed in terms of the prime factorization of V.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Advanced Graph Theory Research
Mathematics and Applications
Publication details
- Journal / source
- Ars Combinatoria
- Volume
- 167
- Pages
- 3–27
- Publication date
- 9 May 2026
- Language
- EN