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ISRN Discrete Mathematics
Volume 2012 (2012), Article ID 308595, 8 pages
http://dx.doi.org/10.5402/2012/308595
Research Article

Bipancyclic Properties of Faulty Hypercubes

Department of Computer Science and Information Engineering, Da-Yeh University, Changhua 51591, Taiwan

Received 24 July 2012; Accepted 5 September 2012

Academic Editors: L. Ji, U. Vaccaro, W. Wallis, and X. Yong

Copyright © 2012 Chun-Nan Hung and Min-Kun Hsiao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A bipartite graph is bipancyclic if it contains cycles of every even length from 4 to and edge bipancyclic if every edge lies on a cycle of every even length from 4 to . Let denote the -dimensional hypercube. Let be a subset of such that can be decomposed into two parts and , where is a union of disjoint adjacent pairs of , and consists of edges. We prove that is bipancyclic if . Moreover, is edge bipancyclic if with .