Fundamental Groups of Hamming Graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916696791449600 |
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| author | Behal, Keira Chih, Tien |
| author_facet | Behal, Keira Chih, Tien |
| contents | Recently there has been growing interest in discrete homotopies and homotopies of graphs beyond treating graphs as 1-dimensional simplicial spaces. One such type of homotopy is $\times$-homotopy. Recent work by Chih-Scull has developed a homotopy category, a fundamental group for graphs under this homotopy, and a way of computing covers of graphs that lift homotopy via this fundamental group. In this paper, we compute the fundamental groups of all Hamming graphs, show that they are direct products of cyclic groups, and use this result to describe some $\times$-homotopy covers of Hamming graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_02938 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fundamental Groups of Hamming Graphs Behal, Keira Chih, Tien Combinatorics 05C25 05C25 05C25 05C25, 05C76, 05E18 Recently there has been growing interest in discrete homotopies and homotopies of graphs beyond treating graphs as 1-dimensional simplicial spaces. One such type of homotopy is $\times$-homotopy. Recent work by Chih-Scull has developed a homotopy category, a fundamental group for graphs under this homotopy, and a way of computing covers of graphs that lift homotopy via this fundamental group. In this paper, we compute the fundamental groups of all Hamming graphs, show that they are direct products of cyclic groups, and use this result to describe some $\times$-homotopy covers of Hamming graphs. |
| title | Fundamental Groups of Hamming Graphs |
| topic | Combinatorics 05C25 05C25 05C25 05C25, 05C76, 05E18 |
| url | https://arxiv.org/abs/2308.02938 |