Randic energy of specific graphs

Let $G$ be a simple graph with vertex set $V(G)=\{v_1,v_2,\mathrm{.}\mathrm{.}\mathrm{.},v_n\}$. The Randi'{c} matrix of $G$, denoted by $R(G)$, is defined as the $n\times n$ matrix whose $(i,j)$-entry is $(d_i{d}_j{)}^{\frac{-1}{2}}$ if $v_i$ and $v_j$ are adjacent and $0$ for another cases. Let the eigenvalues of the Randi'{c} matrix $R(G)$ be ${\rho }_1\ge {\rho }_2\ge \mathrm{.}\mathrm{.}\mathrm{.}\ge {\rho }_n$ which are the roots of the Randi'c characteristic polynomial ${\prod }_{i=1}^n(\rho -{\rho }_i)$. The Randi'{c} energy $RE$ of $G$ is the sum of absolute values of the eigenvalues of $R(G)$. In this paper we compute the Randi'c characteristic polynomial and the Randi'c energy for specific graphs $G$.