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Bipanconnectivity and Bipancyclicity in k-ary n-cubes
January 2009 (vol. 20 no. 1)
pp. 25-33
ASCII Text
x 
 
Iain A. Stewart, Yonghong Xiang, "Bipanconnectivity and Bipancyclicity in k-ary n-cubes," IEEE Transactions on Parallel and Distributed Systems, vol. 20, no. 1, pp. 25-33, January, 2009.
 
 
BibTex
x
 
@article{ 10.1109/TPDS.2008.45,
author = {Iain A. Stewart and Yonghong Xiang},
title = {Bipanconnectivity and Bipancyclicity in k-ary n-cubes},
journal ={IEEE Transactions on Parallel and Distributed Systems},
volume = {20},
number = {1},
issn = {1045-9219},
year = {2009},
pages = {25-33},
doi = {http://doi.ieeecomputersociety.org/10.1109/TPDS.2008.45},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Parallel and Distributed Systems
TI - Bipanconnectivity and Bipancyclicity in k-ary n-cubes
IS - 1
SN - 1045-9219
SP25
EP33
EPD - 25-33
A1 - Iain A. Stewart,
A1 - Yonghong Xiang,
PY - 2009
KW - Interconnection architectures
KW - Path and circuit problems
VL - 20
JA - IEEE Transactions on Parallel and Distributed Systems
ER -
 
Iain A. Stewart, University of Durham, Durham
Yonghong Xiang, University of Durham, Durham
In this paper we give precise solutions to problems posed by Wang, An, Pan, Wang and Qu and by Hsieh, Lin and Huang. In particular, we show that Qnk is bipanconnected and edge-bipancyclic, when k ≥ 3 and n ≥ 2, and we also show that when k is odd, Qnk is m-panconnected, for m=(n(k-1)+2k-6)/2, and (k-1)-pancyclic (these bounds are optimal). We introduce a path-shortening technique, called progressive shortening, and strengthen existing results, showing that when paths are formed using progressive shortening then these paths can be efficiently constructed and used to solve a problem relating to the distributed simulation of linear arrays and cycles in a parallel machine whose interconnection network is Qnk, even in the presence of a faulty processor.

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Index Terms:
Interconnection architectures, Path and circuit problems
Citation:
Iain A. Stewart, Yonghong Xiang, "Bipanconnectivity and Bipancyclicity in k-ary n-cubes," IEEE Transactions on Parallel and Distributed Systems, vol. 20, no. 1, pp. 25-33, Jan. 2009, doi:10.1109/TPDS.2008.45
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