Maximum values of the Sombor-index-like graph invariants of trees and connected graphs

Abstract

A set of novel vertex-degree-based invariants was introduced by Gutman, denoted by \newline $S{O}_1,S{O}_2,\dots ,S{O}_6$. 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 $S{O}_5$ and $S{O}_6$ in the set of molecular trees with a given number of vertices, respectively, and we have found the maximum value of $S{O}_5$ in a class of connected graphs.

11 pages