Some classes of uniquely 3-colorable graphs

In this paper we shall present the concept of a uniquely n-colorable graph, and then introduce a class of graphs which we shall call 6-clique rings. We shall show that 6-clique rings are useful in generating some classes of uniquely 3-colorable graphs. Moreover, we shall demonstrate how the techniques used in producing uniquely 3-colorable graphs from 6-clique rings can be extended to allow the production of other classes of uniquely 3-colorable graphs as well as the production of uniquely n-colorable graphs, where n>3.