Efficient Algorithms for Embedding Cycles in Augmented Cubes

Many parallel and distributed algorithms have been developed using such regular data structure as linear arrays, rings, trees, and meshes on hypercube-type interconnection networks. The augmented cube AQ_n, proposed by Choudum and Sunitha, is a derivative of hypercubes with good geometric nature and retains all the favorable properties of the hypercube. The pancyclic properties of the n-dimensional augmented cube, AQ_n, has attracted a lot of interest. In this paper, we introduce the augmented Gray code, AGC, and use AGC to construct cycles of arbitrary number of vertices into the augmented cube for any specific edge.