Maximum randić energy of unicyclic graphs

Given a graph G = (V, E) , the randić   matrix of G is R(G) = (r_{ij}) , where r_{ij}=\frac{۱}{\sqrt{d_{v_i}d_{v_j}}} if v_iv_j \in E(G) and ۰ 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.

کلیدواژه ها:

characteristic polynomial ، Energy ، Randi\'c matrix