Analysis on the Component Connectivity of Enhanced Hypercubes

Abstract

Abstract Reliability evaluation of interconnection networks is of significant importance to the design and maintenance of interconnection networks. The component connectivity is an important parameter for the reliability evaluation of interconnection networks and is a generalization of the traditional connectivity. 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. Determining the $g$-component connectivity is still an unsolved problem in many interconnection networks. Let $Q_{n,k}$ ($1\leq k\leq n-1$) denote the $(n, k)$-enhanced hypercube. In this paper, let $n\geq 7$ and $1\leq k \leq n-5$, we determine $c\kappa _{g}(Q_{n,k}) = g(n + 1) - \frac{1}{2}g(g + 1) + 1$ for $2 \leq g \leq n$. The previous result in Zhao and Yang (2019, Conditional connectivity of folded hypercubes. Discret. Appl. Math., 257, 388–392) is extended.