The Relation on the Coefficients and Roots of Adjoint Polynomial and Its Application

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(Dn),where β(G) is the minimum root of the adjoint polynomial of graph G and the chromatically equivalent classification of tDn is completely depicted.Furthermore,a sufficient and necessary condition for the class of graphs to be chromatically unique is obtained.