The g-Extra Conditional Diagnosability of Graphs in Terms of g-Extra Connectivity

Abstract

The [Formula: see text]-extra conditional diagnosability and [Formula: see text]-extra connectivity are two important parameters to measure ability of diagnosing faulty processors and fault tolerance in a multiprocessor system. The [Formula: see text]-extra conditional diagnosability [Formula: see text] of graph [Formula: see text] is defined as the diagnosability of a multiprocessor system under the assumption that every fault-free component contains more than [Formula: see text] vertices. While the [Formula: see text]-extra connectivity [Formula: see text] of graph [Formula: see text] is the minimum number [Formula: see text] for which there is a vertex cut [Formula: see text] with [Formula: see text] such that every component of [Formula: see text] has more than [Formula: see text] vertices. In this paper, we study the [Formula: see text]-extra conditional diagnosability of graph [Formula: see text] in terms of its [Formula: see text]-extra connectivity, and show that [Formula: see text] under the MM* model with some acceptable conditions. As applications, the [Formula: see text]-extra conditional diagnosability is determined for some BC networks such as hypercubes, varietal hypercubes, and [Formula: see text]-ary [Formula: see text]-cubes under the MM* model.