Fault-free vertex-pancyclicity in faulty augmented cubes
نویسنده
چکیده
The n-dimensional augmented cube, denoted as AQn, a variation of the hypercube, possesses some properties superior to those of the hypercube. In this paper, we show that every vertex in AQn lies on a fault-free cycle of every length from 3 to 2, even if there are up to n − 1 link faults. We also show that our result is optimal.
منابع مشابه
Geodesic-pancyclicity and fault-tolerant panconnectivity of augmented cubes
Choudum and Sunitha [Networks 40 (2002) 71–84] proposed the class of augmented cubes as a variation of hypercubes and showed that augmented cubes possess several embedding properties that the hypercubes and other variations do not possess. Recently, Hsu et al. [Information Processing Letters 101 (2007) 227–232] showed that the ndimensional augmented cube AQn, n 2, is weakly geodesic-pancyclic, ...
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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 ...
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As an enhancement on the hypercube Qn, the augmented cube AQn, prosed by Choudum and Sunitha [S.A. Choudum, V. Sunitha, Augmented cubes, Networks 40 (2) (2002) 71–84], not only retains some favorable properties of Qn but also possesses some embedding properties that Qn does not. For example, AQn is pancyclic, that is, AQn contains cycles of arbitrary length for n 2. This paper shows that AQn re...
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تاریخ انتشار 2009