Large trees with maximal inverse sum indeg index have no vertices of degree 2 or 3

Abstract

The inverse sum indeg ($ISI$) index has attracted more and more attentions, because of its significant applications in chemistry. A basic problem in the study of this topological index is the characterization trees with maximal $ISI$ value. Let $T$ be such a tree of order $n\ge 20$. Recently, Lin et al. (2022) claimed that $T$ has no vertices of degree 2. However, errors were found in their proofs. Since this result is quite important, we give a correction to the proof. Furthermore, we extend the result by proving that $T$ has no vertices of degree 2 or 3 if $n\ge 58$.