Abstract
Crossed cubes network is a kind of interconnection structure as a basis for distributed memory parallel computer architecture. Reliability takes an important role in fault tolerant computing on multiprocessor systems. Connectivity is a vital metric to explore fault tolerance and reliability of network structure based on a graph model. Let be a connected graph. The k-conditional edge connectivity is the cardinality of the minimum edge cuts , if any, whose deletion disconnects and each component of has property of minimum degree . The k-conditional connectivity can be defined similarly. In this paper, we determine the k- conditional (edge) connectivity of crossed cubes for small k. And we also prove other properties of .
Highlights
With the development of VLSI technology and software technology, multiprocessor systems with hundreds of thousands of processors have become available
Crossed cubes network is a kind of interconnection structure as a basis for distributed memory parallel computer architecture
Reliability takes an important role in fault tolerant computing on multiprocessor systems
Summary
With the development of VLSI technology and software technology, multiprocessor systems with hundreds of thousands of processors have become available. Let G = (V , E) be a connected graph. We determine the kconditional (edge) connectivity of crossed cubes CQn for small k. The conditional edge connectivity λ(G, P) or conditional connectivity κ (G, P) is the minimum cardinality of a set of edges or vertices, if it exists, whose deletion disconnects G and each remaining component has property P .
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