The conjecture about the comparison for resolvent energies of cycles and stars

The resolvent energy of a graph G of order n is defined as ER(G) = Pn i=1 (n - Σi)-1, where λ1; λ2; : : : ; λn are the eigenvalues of G. Gutman et al. [Resolvent energy of graphs, MATCH Commun. Math. Comput. Chem. 75 (2016) 279-290] proposed a conjecture that ER(Sn) < ER(Cn) holds for all n ≥ 4, where Sn and Cn are the star and the cycle of order n, respectively. In this note, we confirm this conjecture.