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arXiv · 2506.14240

Neighbor Connectivity of Undirected Toroidal Meshes

Hui-Ming Huang·Ruichao Niu·Min Xu·Jou-Ming Chang
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Abstract

In this paper, we examine the neighbor connectivity, denoted as $\kappa_{NB}$, of the undirected toroidal mesh $C(d_1,d_2,\ldots,d_n)$. We demonstrate that $\kappa_{NB}(C(d_1,d_2,\ldots,d_n)) = n$ 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.

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Hui-Ming Huang, Ruichao Niu, Min Xu, Jou-Ming Chang. 2025-06-17. Neighbor Connectivity of Undirected Toroidal Meshes. https://arxiv.org/abs/2506.14240

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