On Sombor index of trees

Abstract

This paper is concerned with the recently introduced Sombor index SO, defined as SO=SO(G)=∑vkvℓ∈E(G)dG(vk)2+dG(vℓ)2,where dG(v) is the degree of the vertex v of a graph G. We present bounds on SO of trees in terms of order, independence number, and number of pendent vertices, and characterize the extremal cases. In addition, analogous results for quasi-trees are established.