  A set of novel vertex-degree-based invariants was introduced by Gutman,
denoted by \newline $SO_1, SO_2, \ldots,SO_6$. These invariants were
constructed through geometric reasoning based on a new graph invariant
framework. Motivated by proposed open problems in [Z. Tang, Q. Li, H. Deng,
\textit{Trees with Extremal Values of the Sombor-Index-Like Graph Invariants},
MATCH Commun. Math. Comput. Chem. \textbf{90} (2023) 203-222], we have found
the maximum values of $SO_5$ and $SO_6$ in the set of molecular trees with a
given number of vertices, respectively, and we have found the maximum value of
$SO_5$ in a class of connected graphs.
