The h-Restricted Connectivity of a Class of Hypercube-Based Compound Networks

Abstract

Abstract For the multiprocessor systems modeled by interconnection networks, one of the important properties is the characterization of fault tolerability. Connectivity, as an important parameter to evaluate fault tolerability, has witnessed research achievements. To make the evaluation more practical, conditional connectivity has been promisingly proposed. As one kind of conditional connectivity, $h$-restricted connectivity of a connected graph $G$, denoted by $\kappa ^h (G)$, is defined as the cardinality of the minimum vertex cut set $F$ such that $\delta (G-F)\geq h$. In this paper, we establish a universally $h$-restricted connectivity for a class of hypercube-based compound networks, in which the well-known networks, such as hierarchical cubic network $HCN(n, n)$ and its generalization complete cubic network $CCN(n)$, are involved.