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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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| _version_ | 1866913563650555904 |
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| author | Bille, Artur Buchstaber, Victor Spodarev, Evgeny |
| author_facet | Bille, Artur Buchstaber, Victor Spodarev, Evgeny |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19322 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some open mathematical problems on fullerenes Bille, Artur Buchstaber, Victor Spodarev, Evgeny Combinatorics Spectral Theory 92E10 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. |
| title | Some open mathematical problems on fullerenes |
| topic | Combinatorics Spectral Theory 92E10 |
| url | https://arxiv.org/abs/2410.19322 |