UM
On the path-connectivity, vertex-pancyclicity, and edge-pancyclicity of crossed cubes
Yang X.3; Evans D.J.4; Megson G.M.1; Tang Y.3
2005-03-01
Source PublicationNeural, Parallel and Scientific Computations
ISSN10615369
Volume13Issue:1Pages:107-118
AbstractCrossed cube architecture is an alternative to interconnection network due to its half diameter and better graph embedding capability compared with hypercube of the same size. Path and cycle structures are essential for parallel computation since many typical problems can be efficiently solved on these structures. This paper addresses the existence of paths or cycles with specified properties in an n-dimensional crossed cube, CQ. We first propose the notions of path-connectivity, vertex-pancyclicity, and edge-pancyclicity for a graph. We then prove that for any two distinct vertices on CQ at a distance of d apart and each integer l satisfying d + 2 ≤ l ≤ V(CQ) - 1, CQ has a path of length l between this pair of vertices. Based on this, we conclude that (1) for each vertex on CQ and each integer l satisfying 4 ≤ l ≤ V(CQ) , CQ has a cycle of length l that contains this vertex, and (2) for each edge of CQ and each integer l satisfying 4 ≤ l ≤ V(CQ) , CQ has a cycle of length l that contains this edge. Due to the fact that hypercubes do not share these properties, crossed cubes show more advantages over hypercubes. © Dynamic Publishers, Inc.
KeywordConnectivity Crossed cube Interconnection network Pancyclicity
URLView the original
Language英語
Fulltext Access
Document TypeJournal article
CollectionUniversity of Macau
Affiliation1.University of Reading
2.Hong Kong Baptist University
3.Chongqing University
4.Loughborough University
Recommended Citation
GB/T 7714
Yang X.,Evans D.J.,Megson G.M.,et al. On the path-connectivity, vertex-pancyclicity, and edge-pancyclicity of crossed cubes[J]. Neural, Parallel and Scientific Computations,2005,13(1):107-118.
APA Yang X.,Evans D.J.,Megson G.M.,&Tang Y..(2005).On the path-connectivity, vertex-pancyclicity, and edge-pancyclicity of crossed cubes.Neural, Parallel and Scientific Computations,13(1),107-118.
MLA Yang X.,et al."On the path-connectivity, vertex-pancyclicity, and edge-pancyclicity of crossed cubes".Neural, Parallel and Scientific Computations 13.1(2005):107-118.
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