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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.18593 |
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| _version_ | 1866912878249902080 |
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| author | Sadahiro, Taizo |
| author_facet | Sadahiro, Taizo |
| contents | We show that the star graph defined as the Cayley graph of ${\mathfrak S}_{n+1}$ generated by the star transpositions is an ${\mathfrak S}_n$-cover of the complete graph $K_{n+1}$, which is known to have fine spectral properties. In the case $n = 3$, the star graph also has fine geometric properties: it embeds into the honeycomb lattice and has a spectrum computable via both representation theory and an explicit Fourier formula. Intermediate covers correspond to the cube and truncated tetrahedron, offering a new interpretation of their integral spectra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18593 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An ${\mathfrak S}_3$-cover of $K_4$ and integral polyhedral graphs Sadahiro, Taizo Combinatorics We show that the star graph defined as the Cayley graph of ${\mathfrak S}_{n+1}$ generated by the star transpositions is an ${\mathfrak S}_n$-cover of the complete graph $K_{n+1}$, which is known to have fine spectral properties. In the case $n = 3$, the star graph also has fine geometric properties: it embeds into the honeycomb lattice and has a spectrum computable via both representation theory and an explicit Fourier formula. Intermediate covers correspond to the cube and truncated tetrahedron, offering a new interpretation of their integral spectra. |
| title | An ${\mathfrak S}_3$-cover of $K_4$ and integral polyhedral graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2508.18593 |