Extremal vertex-degree function index of trees with some given parameters

Abstract

Recently, Gutman constructed six novel graph invariants in view of geometric arguments and defined them as Sombor-index-like graph invariants, denoted by $SO_{1},SO_{2},\cdots, SO_{6}$. In this article, we obtain a lower bound on four Sombor-index-like graph invariants ($SO_{1},SO_{2}, SO_{5}$ and $SO_{6}$) 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.