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Section A

The bicube: an interconnection of two hypercubes

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Pages 29-40 | Received 06 May 2013, Accepted 29 Jan 2014, Published online: 27 Mar 2014
 

Abstract

We consider two definitions of the even-dimensional hypercube given in the literature. The labelled graphs obtained by two definitions are not same, but one is isomorphic to the other. By interconnecting two labelled graphs in such a way that each pair of vertices with the same label are joined by an edge, we construct a vertex-symmetric graph with the diameter about half that of a comparable hypercube. We extend the result to a general scheme for interconnecting two hypercubes to produce a network topology called the bicube. We show that the bicube preserves the vertex-symmetry, bipartiteness, hamiltonian and bipancyclic properties of the hypercube, and is highly edge-symmetric.

2010 AMS Subject Classifications::

Acknowledgement

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2013R1A1A2012890).

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