On circulant chromatic number and circulant chromatic function Original Research Article

A new concept of circulant chromatic function of a graph is introduced to generalize the concept of chromatic polynomial of a graph. This is similar to the generalization from the concept of chromatic number to the concept of circulant chromatic number. We provide circulant chromatic functions for a few classes of graphs. We consider circulant chromatic functions on the graphs obtained by elementary operations on given graphs, and the relationship between the circulant chromatic number of a graph and that of its complement. We also investigate some sufficient conditions for the circulant chromatic number and the chromatic number of a graph to be equal to each other.