The characteristic polynomial of a graph $G$ with $p$ vertices is defined as $\phi(G: \lambda) = \det(\lambda I - A(G))$, where $A$ is the adjacency matrix of $G$ and $I$ is the unit matrix. The roots of the characteristic equation $hi(G: ambda) = 0$, denoted by $ambda_1, ambda_2, ..., ambda_p$ are the eigenvalues of $G$. The graphs with large number of edges are referred as graph representations of inorganic clusters, called as Cluster graphs. In this paper we obtain the characteristic polynomial of class of cluster graphs.