The Conditional Diagnosability of Exchanged Crossed Cube

Abstract

Conditional diagnosability is widely accepted as an important measure in determining the reliability of an interconnection network. The conditional diagnosability of many well-known interconnection networks has been investigated. Exchanged crossed cube(ECQ(s,t)) is a novel variant of hypercube, which retains the advantages of exchanged hypercube and crossed cube in terms of the smaller diameter, fewer links, and lower cost factor, and indicates more balanced consideration among performance and cost. In this paper, several topological properties of ECQ(s,t) are derived. On this basis, the conditional diagnosability of ECQ(s,t) under the PMC model is shown to be <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4(s-1)+1$ </tex-math></inline-formula> for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t\ge s&gt;2$ </tex-math></inline-formula> , which is almost two times larger than its classical diagnosability and also is larger than its conditional diagnosability under the MM model.