Neighbor Connectivity of Undirected Toroidal Meshes

Abstract

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