This paper presents results on the chromatic polynomials of some graphs. In particular, the chromatic polynomials of  and corona are obtained. Interestingly, the chromatic polynomial of  is an alternating series involving binomial coefficients. In addition, the chromatic polynomial of the corona of graphs is also obtained. As a consequence, the chromatic number  of every graph G considered in this paper is obtained.

chromatic number, chromatic polynomial, coloring.