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arXiv · 2305.02925

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

Milan Bašić
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Abstract

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.

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Milan Bašić. 2023-05-04. Maximum values of the Sombor-index-like graph invariants of trees and connected graphs. https://arxiv.org/abs/2305.02925

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