EXTREMAL VALUES ON THE MODIFIED SOMBOR INDEX OF TREES AND UNICYCLIC GRAPHS - Raghavendra H Kashyap; Yanamandram B Venkatakrishnan; Rashad Ismail; Selvaraj Balachandran; Hari Naresh Kumar (Ural Mathematical Journal)
Let \(G=(V,E)\) be a simple connected graph. The modified Sombor index denoted by \(mSo(G)\) is defined as $$mSo(G)=\sum_{uv\in E}\frac{1}{\sqrt{d^2_u+d^2_v}},$$ where \(d_v\) denotes the degree of vertex \(v\). In this paper we present extremal values of modified Sombor index  over the set of trees and unicyclic graphs.