Acta Mathematica Sinica, English Series

, Volume 26, Issue 7, pp 1315–1322 | Cite as

Edge-pancyclicity and Hamiltonian connectivity of twisted cubes

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Abstract

The twisted cube TQ n is a variant of the hypercube Q n . It has been shown by Chang, Wang and Hsu [Topological properties of twisted cube. Information Science, 113, 147–167 (1999)] that TQ n contains a cycle of every length from 4 to 2 n . In this paper, we improve this result by showing that every edge of TQ n lies on a cycle of every length from 4 to 2 n inclusive. We also show that the twisted cube are Hamiltonian connected.

Keywords

cycles twisted cubes hypercubes edge-pancyclicity hamiltonian connectivity 

MR(2000) Subject Classification

05C38 90B10 
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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Laboratory of Mathematics and Complex Systems, Ministry of EducationSchool of Mathematical Sciences, Beijing Normal UniversityBeijingP. R. China

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