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The resolvent energy of a graph $G$ of order $n$ is defined as$ER=\sum_{i=1}^n (n-\lambda_i)^{-1}$, where$\lambda_1,\lambda_2,\ldots,\lambda_n$ are the eigenvalues of $G$. In a recentwork [Gutman et al., {\it MATCH Commun. Math. Comput. Chem.\/} {\bf 75} (2016)279--290] the structure of the graphs extremal w.r.t. $ER$ were conjectured,based on an extensive computer--aided search. We now confirm the validity ofsome of these conjectures.

Resolvent Energy of Unicyclic, Bicyclic and Tricyclic Graphs