On g-Extra Conditional Diagnosability of Twisted Hypercubes under MM∗ Model

Abstract

Connectivity and diagnosability are important parameters in measuring the reliability and fault-tolerance of an interconnection network [Formula: see text]. The [Formula: see text]-extra conditional faulty set [Formula: see text] is a faulty vertex set such that every component of [Formula: see text] has at least [Formula: see text] vertices. The [Formula: see text]-extra connectivity [Formula: see text] of a connected graph [Formula: see text] is the minimum cardinality of a [Formula: see text]-extra conditional faulty set [Formula: see text] of [Formula: see text] such that [Formula: see text] is disconnected. The [Formula: see text]-extra conditional diagnosability [Formula: see text] of a graph [Formula: see text] is the maximum value of [Formula: see text] such that [Formula: see text] is [Formula: see text]-extra conditionally [Formula: see text]-diagnosable. The [Formula: see text]-extra connectivity of [Formula: see text] is necessary for [Formula: see text]-extra diagnosability of [Formula: see text]. The [Formula: see text]-dimensional twisted hypercube [Formula: see text] is a new variant of hypercubes with asymptotically optimal diameter. In this paper, we first give the [Formula: see text]-extra connectivity of [Formula: see text] for [Formula: see text] and [Formula: see text]; and then obtain the [Formula: see text]-extra conditional diagnosability of [Formula: see text] for [Formula: see text] and [Formula: see text] under the MM[Formula: see text] model.