On chromatic polynomial of certain families of dendrimer graphs

Let G be a simple graph with vertex set V ( G ) and edge set E ( G ) . A mapping g : V ( G ) → { 1 , 2 , … t } is called t -coloring if for every edge e = ( u , v ) , we have g ( u ) ≠ g ( v ) . The chromatic number of the graph G is the minimum number of colors that are required to properly color the graph. The chromatic polynomial of the graph G , denoted by P ( G , t ) is the number of all possible proper coloring of G . Dendrimers are hyper-branched macromolecules, with a rigorously tailored architecture. They can be synthesized in a controlled manner either by a divergent or a convergent procedure. Dendrimers have gained a wide range of applications in supra-molecular chemistry, particularly in host guest reactions and self-assembly processes. Their applications in chemistry, biology and nano-science are unlimited. In this paper, the chromatic polynomials for certain families of dendrimer nanostars have been computed.