فهرست نشریات علمی دسترسی آزاد ایران

Given a graph $ G = (V, E) $, the randić   matrix of $G$ is $ R(G) = (r_{ij}) $, where $r_{ij}=\frac{1}{\sqrt{d_{v_i}d_{v_j}}}$ if $v_iv_j \in E(G)$ and $0$ otherwise, and $ d_{v_i}$ is the degree of the vertex $ v_{i} $ in $ G$. The randić  energy is the sum of absolute values of the eigenvalues of randić  matrix. The $R$-polynomial of $ G $ is defined by $ \phi_{R} (G, x)=det(xI_{n}-R(G)) $. In this paper, we obtain the $R$-polynomial as well as the randić  energy of a unicyclic graph. In particular, we determine all unicyclic graphs with maximum randić  energy.