Reliability evaluation of folded hypercubes in terms of component connectivity

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 $c{\kappa }_g(F{Q}_n)=g(n+1)-\frac{1}{2}g(g+1)+1$ for $1\le g\le n+1,n\ge 8$ in this paper.

The work was included in the MS thesis of the first author in [On the component connectiviy of hypercubes and folded hypercubes, MS Thesis at Taiyuan University of Technology, June 2017]