Neighbor Connectivity of Undirected Toroidal Meshes

TL;DR

This paper investigates the neighbor connectivity of undirected toroidal meshes, establishing a theoretical value and supporting it with computer simulations to deepen understanding of their structural properties.

Contribution

It provides a precise theoretical determination of neighbor connectivity in undirected toroidal meshes and validates it through computer simulations.

Findings

Neighbor connectivity $$ equals the number of dimensions $n$ for all $d_i \u2265 3$.

Computer simulations support the theoretical results.

Deeper insights into neighbor structure failures in these 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.