  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 recent
work [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 of
some of these conjectures.
