Multiplicative Sombor Index of Graphs

Abstract

The Sombor index of a graph G is defined as SO ( G ) = (cid:80) uv ∈ E ( G ) (cid:112) d 2 G ( u ) + d 2 G ( v ) , where d G ( u ) denotes the degree of the vertex u of G . Accordingly, the multiplicative Sombor index of G can be defined as (cid:81) SO ( G ) = (cid:81) uv ∈ E ( G ) (cid:112) d 2 G ( u ) + d 2 G ( v ) . In this article, some graph transformations which increase or decrease the multiplicative Sombor index are first introduced. Then by using these transformations, extremal values of the multiplicative Sombor index of trees and unicyclic graphs are determined.