A Note on a Kind of Conditional Connectivity with Application to Hypercube

Connectivity is a vital parameter to measure the reliability and fault tolerability of the multiprocessor systems. To better characterize system reliability of resisting the block-based attacks, some structural connectivities have been proposed successively. In this paper, we propose a novel kind of structural connectivity based the cyclic fault pattern, called cyclic fault-block connectivity. Let [Formula: see text] be a connected graph and [Formula: see text]. Then [Formula: see text] is called a cyclic fault-block cut of [Formula: see text] if [Formula: see text] is disconnected so that at least two components of [Formula: see text] contain cycles and [Formula: see text] is connected. The minimum cardinality over all cyclic fault-block cuts of [Formula: see text] is called cyclic fault-block connectivity of [Formula: see text], denoted by [Formula: see text]. Furthermore, we show that the cyclic fault-block connectivity of [Formula: see text] is [Formula: see text] for [Formula: see text].