caa a22 4500 445852046 CHVBK 20180317145416.0 cr unu---uuuuu 170323e20110501xx s 000 0 eng 10.1007/s11227-009-0356-8 doi (NATIONALLICENCE)springer-10.1007/s11227-009-0356-8 Panconnectivity of Cartesian product graphs [Elektronische Daten] [You Lu, Jun-Ming Xu] A graph G of order n(≥2) is said to be panconnected if for each pair (x,y) of vertices of G there exists an xy-path of length ℓ for each ℓ such that d G(x,y)≤ℓ≤n−1, where d G(x,y) denotes the length of a shortest xy-path in G. In this paper, we consider the panconnectivity of Cartesian product graphs. As a consequence of our results, we prove that the n-dimensional generalized hypercube Q n(k 1,k 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 3-ary n-cube $Q^{3}_{n}$ is panconnected. Springer Science+Business Media, LLC, 2009 Graph theory nationallicence Interconnection networks nationallicence Panconnectivity nationallicence Cartesian product nationallicence Hypercubes nationallicence k -ary n -cubes nationallicence Lu You Department of Mathematics, University of Science and Technology of China, 230026, Hefei, China aut Xu Jun-Ming Department of Mathematics, University of Science and Technology of China, 230026, Hefei, China aut The Journal of Supercomputing Springer US; http://www.springer-ny.com 56/2(2011-05-01), 182-189 0920-8542 56:2<182 2011 56 11227 https://doi.org/10.1007/s11227-009-0356-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11227-009-0356-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lu You Department of Mathematics, University of Science and Technology of China, 230026, Hefei, China aut NATIONALLICENCE 700 1- Xu Jun-Ming Department of Mathematics, University of Science and Technology of China, 230026, Hefei, China aut NATIONALLICENCE 773 0- The Journal of Supercomputing Springer US; http://www.springer-ny.com 56/2(2011-05-01), 182-189 0920-8542 56:2<182 2011 56 11227 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer