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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

10.1007/bf01069046

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1573-0484

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Panconnectivity of Cartesian product graphs

Authors: You Lu JunMing Xu
Publish Date: 2009/11/07
Volume: 56, Issue: 2, Pages: 182-189
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Abstract

A graph G of order n ≥2 is said to be panconnected if for each pair xy of vertices of G there exists an xypath of length ℓ for each ℓ such that d G xy≤ℓ≤n−1 where d G xy denotes the length of a shortest xypath in G In this paper we consider the panconnectivity of Cartesian product graphs As a consequence of our results we prove that the ndimensional generalized hypercube Q n k 1k 2…k n is panconnected if and only if k i ≥3 i=1…n which generalizes a result of Hsieh et al that the 3ary ncube Q3 n is panconnected

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