Abstract
For a graph \(G\) the Sombor index of \(G\) is defined as \(\sum_{uv\in E(G)} \sqrt{d(u)^2+d(v)^2}\), where \(d(u)\) is the degree of \(u\) in \(G\). In the current paper, we study the structure of a graph with minimum Sombor index among all graphs with
fixed order and fixed size. It is shown that in every graph with minimum Sombor index the difference between minimum and maximum degrees is at most 1.