ABSTRACT
This chapter provides various definitions of generalized Gray codes and brings out the intrinsic difference between the Gray codes with odd and even base. The widespread availability of distributed memory architectures based on the binary hypercube topology, there is a growing interest in the portability of algorithms developed for architectures based on other topologies such as linear arrays, rings, multidimensional grids, trees, to hypercube based architectures. While these generalized Gray codes have immediate applications to the embedding of graphs in a base-b cube, the analysis of their properties holds independent interest as well. However, there is a close relation between the cyclic Gray codes and a class of Gray codes called reflected Gray codes.
