Neighbor Connectivity of Undirected Toroidal Meshes
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909651409305600 |
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| author | Huang, Hui-Ming Niu, Ruichao Xu, Min Chang, Jou-Ming |
| author_facet | Huang, Hui-Ming Niu, Ruichao Xu, Min Chang, Jou-Ming |
| contents | In this paper, we examine the neighbor connectivity, denoted as $κ_{NB}$, of the undirected toroidal mesh $C(d_1,d_2,\ldots,d_n)$. We demonstrate that $κ_{NB}(C(d_1,d_2,\ldots,d_n)) = n$ for all $n \ge 2$ and $d_i \ge 3$ (for $1 \le i \le n$). Additionally, we perform a computer simulation experiment on neighbor connectivity in undirected toroidal meshes. This experiment not only supports our theoretical findings with empirical results but also provides a deeper understanding of neighbor structure failures in undirected toroidal meshes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14240 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Neighbor Connectivity of Undirected Toroidal Meshes Huang, Hui-Ming Niu, Ruichao Xu, Min Chang, Jou-Ming Combinatorics In this paper, we examine the neighbor connectivity, denoted as $κ_{NB}$, of the undirected toroidal mesh $C(d_1,d_2,\ldots,d_n)$. We demonstrate that $κ_{NB}(C(d_1,d_2,\ldots,d_n)) = n$ for all $n \ge 2$ and $d_i \ge 3$ (for $1 \le i \le n$). Additionally, we perform a computer simulation experiment on neighbor connectivity in undirected toroidal meshes. This experiment not only supports our theoretical findings with empirical results but also provides a deeper understanding of neighbor structure failures in undirected toroidal meshes. |
| title | Neighbor Connectivity of Undirected Toroidal Meshes |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.14240 |