Abstract: The parameter R(G) is the function about the front three coefficients of the adjoint polynomial of graph G. In the paper, the range of R(G) is given when β(G)<β(D_n), where β(G) is the minimum root of the adjoint polynomial of graph G and the chromatically equivalent classification of tD_n is completely depicted. Furthermore,a sufficient and necessary condition for the class of graphs to be chromatically unique is obtained.

Key words: chromatically equivalent, adjoint polynomial, the least root