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\iteman{io-port 05285934}
\itemau{Huang, Chien-Hung; Fang, Jywe-Fei}
\itemti{The pancyclicity and the Hamiltonian-connectivity of the generalized base-$b$ hypercube.}
\itemso{Comput. Electr. Eng. 34, No. 4, 263-269 (2008).}
\itemab
Summary: 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\geqslant $ 3. That is, there exists a Hamiltonian path joining each pair of vertices in a generalized base-$b$ hypercube for $b\geqslant $ 3. We also show that a generalized base-$b$ hypercube is pancyclic for $b\geqslant $ 3. That is, it embeds cycles of all lengths ranging from 3 to the order of the graph for $b\geqslant $ 3.
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\itemut{interconnection networks; hypercubes; pancyclicity; Hamiltonian-connectivity}
\itemli{doi:10.1016/j.compeleceng.2007.05.011}
\end