Magic property of fullerenes
Abstract
Fullerenes are an allotrope of carbon having a hollow, cage-like structure. The atoms in the molecule are arranged in pentagonal and hexagonal rings such that each atom is connected to three other atoms. Simple polyhedra having only pentagonal and hexagonal faces are a mathematical model for fullerenes. We say that a fullerene with n vertices has a magic property if the numbers 1,2,...,n may be assigned to its vertices so that the sums of the numbers on each pentagonal face are equal and the sums of the numbers in each hexagonal face are equal. We show that C8n+4 does not admit such an arrangement for all n, while there are fullerenes, like C24 and C26 that have many nonisomorphic such arrangements.
Fields of Study & Subjects
Graph Labeling and Dimension Problems
Advanced Combinatorial Mathematics
Advanced Graph Theory Research
Publication details
- Journal / source
- Az Eszterházy Károly Tanárképző Főiskola tudományos közleményei. Tanulmányok a matematikai tudományok köréből/Az Eszterházy Károly Főiskola tudományos közleményei. Tanulmányok a matematikai tudományok köréből/Annales mathematicae et informaticae
- Volume
- Accepted manuscript
- Publication date
- 1 January 2026
- Language
- EN