Trees with Extremal Values of the Sombor-Index-Like Graph Invariants

A new geometric background of graph invariants was introduced by Gutman, using the triangle formed by the degree-point, dual-degree-point, and the origin of the coordinate system, a number of new Sombor-index-like VDB invariants, denoted by SO1, SO2, ... , SO6, were constructed by means of geometric arguments. In this paper, the chemical applicability of these Sombor-index-like graph invariants is investigated, and it is shown that almost all of these six indices are useful in predicting physicochemical properties with high accuracy compared to some well-established and often used indices. Also, we obtain a bound for some of the Sombor-index-like graph invariants among all (molecular) trees with fixed numbers of vertices, and characterize those (molecular) trees achieving the extremal value.