On four Sombor-index-like graph invariants of chemical graphs with a given order, number of edges and pendent vertices

Recently, Gutman constructed six novel graph invariants in view of geometric arguments and defined them as Sombor-index-like graph invariants, denoted by S1O, S2O,???, S6O. Compared with some popular and commonly used indices, nearly all these six graph invariants have high accuracy in predicting physical and chemical properties. Therefore, in this article, we obtain a lower bound on four Sombor-index-like graph invariants (S1O, S2O, S5O and S6O) for all chemical (n, m, k)-graphs (chemical graphs of order n having m edges and k pendent vertices), and characterize those chemical (n, m, k)-graphs achieving the extremal value.