On 3-extra connectivity of k-ary n-cubes

TL;DR

This paper investigates the h-extra connectivity of k-ary n-cube networks, specifically determining the case for h=3, which enhances understanding of network robustness and fault tolerance.

Contribution

The paper extends previous work by explicitly calculating the 3-extra connectivity of k-ary n-cubes, a case not previously addressed.

Findings

Derived the 3-extra connectivity for k-ary n-cubes

Extended the theoretical understanding of network fault tolerance

Provided formulas for specific network parameters

Abstract

Given a graph G, a non-negative integer h and a set of vertices S, the h-extra connectivity of G is the cardinality of a minimum set S such that G-S is disconnected and each component of G-S has at least h+1 vertices. The 2-extra connectivity of k-ary n-cube is gotten by Hsieh et al. in [Theoretical Computer Science, 443 (2012) 63-69]. In this paper, we obtained the h-extra connectivity of the k-ary n-cube networks for h=3.