Enumeration formulas for (3, 6)-fullerenes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913157411241984 |
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| author | Green, Linda Sreelesh, Yadunand Arora, Saanvi |
| author_facet | Green, Linda Sreelesh, Yadunand Arora, Saanvi |
| contents | 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 $V$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09170 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enumeration formulas for (3, 6)-fullerenes Green, Linda Sreelesh, Yadunand Arora, Saanvi Combinatorics 05C10 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 $V$. |
| title | Enumeration formulas for (3, 6)-fullerenes |
| topic | Combinatorics 05C10 |
| url | https://arxiv.org/abs/2501.09170 |