The pancyclicity and the Hamiltonian-connectivity of the generalized base-b hypercube

Authors:
Chien-Hung Huang;Jywe-Fei Fang
Affiliations:
Department of Computer Science and Information Engineering, National Formosa University, 64 Wen-Hwa Road, Huwei 632, Taiwan, ROC;Department of Digital Content and Technology, National Taichung University, Taichung 403, Taiwan, ROC
Venue:
Computers and Electrical Engineering
Year:
2008

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Abstract

The interconnection network considered in this paper is the generalized base-b hypercube that is an attractive variance of the well-known hypercube. The generalized base-b hypercube is superior to the hypercube in many criteria, such as diameter, connectivity and fault diameter. In this paper, we study the Hamiltonian-connectivity and pancyclicity of the generalized base-b hypercube by the algorithmic approach. We show that a generalized base-b hypercube is Hamiltonian-connected for b=3. That is, there exists a Hamiltonian path joining each pair of vertices in a generalized base-b hypercube for b=3. We also show that a generalized base-b hypercube is pancyclic for b=3. That is, it embeds cycles of all lengths ranging from 3 to the order of the graph for b=3.