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 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 Publication Neural, Parallel and Scientific Computations ISSN 10615369 Volume 13Issue:1Pages:107-118 Abstract Crossed 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. Keyword Connectivity Crossed cube Interconnection network Pancyclicity URL View the original Language 英語 Fulltext Access Document Type Journal article Collection University of Macau Affiliation 1.University of Reading2.Hong Kong Baptist University3.Chongqing University4.Loughborough University Recommended CitationGB/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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