Edge-pancyclicity of twisted cubes

Authors:
Jianxi Fan;Xiaola Lin;Xiaohua Jia;Rynson W. H. Lau
Affiliations:
Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong, China;College of Information Science and Technology, Sun Yat-sen University, Guangzhou, China;Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong, China;Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong, China
Venue:
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Year:
2005

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Abstract

Twisted cubes are attractive alternatives to hypercubes. In this paper, we study a stronger pancyclicity of twisted cubes. We prove that the n-dimensional twisted cube is edge-pancyclic for n ≥ 3. That is, for any (x,y) ∈ E(TQn) (n ≥ 3) and any integer l with 4 ≤ l ≤ 2n, a cycle C of length l can be embedded with dilation 1 into TQn such that (x,y) is in C. It is clear that an edge-pancyclic graph is also a node-pancyclic graph. Therefore, TQn is also a node-pancyclic graph for n ≥ 3.