Maximally Local Connectivity on Augmented Cubes
نویسندگان
چکیده
Connectivity is an important measurement for the fault tolerance in interconnection networks. It is known that the augmented cube AQn is maximally connected, i.e. (2n − 1)-connected, for n ≥ 4. By the classical Menger’s Theorem, every pair of vertices in AQn is connected by 2n − 1 vertex-disjoint paths for n ≥ 4. A routing with parallel paths can speed up transfers of large amounts of data and increase fault tolerance. Motivated by some research works on networks with faults, we have a further result that for any faulty vertex set F ⊂ V(AQn) and |F| ≤ 2n − 7 for n ≥ 4, each pair of non-faulty vertices, denoted by u and v, in AQn − F is connected by min{degf(u), degf(v)} vertex-disjoint fault-free paths, where degf(u) and degf(v) are the degree of u and v in AQn − F, respectively. Moreover, we have another result that for any faulty vertex set F ⊂ V(AQn) and |F| ≤ 4n − 9 for n ≥ 4, there exists a large connected component with at least 2 − |F| − 1 vertices in AQn − F . In general, a remaining large fault-free connected component also increases fault tolerance.
منابع مشابه
Maximally local connectivity and connected components of augmented cubes
Article history: Received 8 August 2008 Received in revised form 21 January 2012 Accepted 8 March 2014 Available online 19 March 2014
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