On Sombor index of extremal graphs

Let G be a finite simple graph. The Sombor index of G isdefined as \sum\nolimits_{uv\in E(G)} \sqrt{d_{u}^{2}+d_{v}^{2}} where d_{u} and d_{v} represent the degrees of vertices u andv in G , respectively. The sum of the absolute values of theadjacency eigenvalues defines the energy of a graph. This paper aimsto enhance the current connections between the Sombor index and theenergy of graphs. Additionally, we provide some upper bounds for theSombor index of triangle-free, square-free, K_r-free andtripartite graphs in terms of order, size and minimum degree.

On Sombor index of extremal graphs Keywords:

C_4-free graph , energy , Sombor index , tripartite graph , triangle-free graph