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Title of Journal: J Supercomput

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Abbravation: The Journal of Supercomputing

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Springer US

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DOI

10.1016/0140-6736(91)91398-E

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1573-0484

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The panconnectivity and the pancycleconnectivity

Authors: ChienHung Huang JyweFei Fang
Publish Date: 2008/12/11
Volume: 50, Issue: 2, Pages: 162-
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Abstract

The interconnection network considered in this paper is the generalized baseb hypercube that is an attractive variant of the wellknown hypercube The generalized baseb hypercube is superior to the hypercube in many criteria such as diameter connectivity and fault diameter In this paper we study the panconnectivity and pancycleconnectivity of the generalized baseb hypercube We show that a generalized baseb hypercube is panconnected for b≥3 That is for each pair of distinct vertices x and y of the ndimensional generalized baseb hypercube GHbn and for any integer l where Distxy≤l≤N−1 there exists a path of the length l joining x and y where N is the order of the graph GHbn and Distxy is the distance between x and y We also show that a generalized baseb hypercube is pancycleconnected for b≥3 That is every two distinct vertices x and y of the graph GHbn are contained by a cycle of every length ranging from the length of the smallest cycle that contains x and y to N

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