Maximum values of the Sombor-index-like graph invariants of connected graphs
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A set of novel vertex-degree-based invariants, similar to the Sombor-index, was introduced by Gutman, denoted by SO_1, SO_2, …,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, Trees with Extremal Values of the Sombor-Index-Like Graph Invariants, MATCH Commun. Math. Comput. Chem. 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 the set of connected graphs.
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