# Reliability evaluation of folded hypercubes in terms of component connectivity

## TL;DR

This paper extends the understanding of the reliability of folded hypercubes by precisely calculating their component connectivity, a key measure of network robustness, for a range of parameters.

## Contribution

It introduces a formula for the (g+1)-component connectivity of folded hypercubes, generalizing previous results on hypercube connectivity.

## Key findings

- Derived the (g+1)-component connectivity formula for folded hypercubes.
- Established the connectivity for g in the range 1 to n+1, with n ≥ 8.
- Enhanced the understanding of network reliability in interconnection networks.

## Abstract

The component connectivity is the generalization of connectivity which is an parameter for the reliability evaluation of interconnection networks. The $g$-component connectivity $c\kappa_{g}(G)$ of a non-complete connected graph $G$ is the minimum number of vertices whose deletion results in a graph with at least $g$ components. The results in [Component connectivity of the hypercubes, International Journal of Computer Mathematics 89 (2012) 137-145] by Hsu et al. determines the component connectivity of the hypercubes. As an invariant of the hypercube, we determine the $(g+1)$-component connectivity of the folded hypercube $c\kappa_{g}(FQ_{n})=g(n+1)-\frac{1}{2}g(g+1)+1$ for $1\leq g \leq n+1, n\geq 8$ in this paper.