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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.19322 |
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Table of Contents:
- Fullerenes are hollow carbon molecules where each atom is connected to exactly three other atoms, arranged in pentagonal and hexagonal rings. Mathematically, they can be combinatorially modeled as planar, 3-regular graphs with facets composed only of pentagons and hexagons. In this work, we outline a few of the many open questions about fullerenes, beginning with the problem of generating fullerenes randomly. We then introduce an infinite family of fullerenes on which the generalized Stone-Wales operation is inapplicable. Furthermore, we present numerical insights on a graph invariant, called \textit{character} of a fullerene, derived from its adjacency and degree matrices. This descriptor may lead to a new method for linear enumeration of all fullerenes.