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

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.