Abstract :
In this paper, the set of all graphs having the same chromatic polynomial as that of the graph consisting of the join of m copies of the paths each of length 3 is determined. Also, it is shown that, for i = 0, 1, the set of all graphs having the same chromatic polynomial (λ - i)P(G; λ) is obtained by applying the two operations, described in the paper, to every graph which has the same chromatic polynomial as that of G. This result is used in the final section to prove a characterization for T-chromatically unique graphs.
