Up to a natural equivalence relation, the set of biautomatic structures on such a graph product bijects to the product of the sets of biautomatic structures on the vertex groups. The set of automatic structures is much richer. Indeed, it is dense in the infinite product of the sets of automatic structures of all conjugates of the vertex groups.
Analogous statements hold for asynchronous automatic structures.
We also discuss the boundaries of these structures. Some useful hints. Get help with viewing preprints on-line. A new window will pop up in which you will be asked to type in the name under which you want to save the file. A new window will pop up in which you will be asked to type in the name under which you want to save the file.