Neighbor Connectivity of Undirected Toroidal Meshes

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.