On the Graphs with Minimum Sombor Index
Aarman Aashtab, Saieed Akbari, Saba Madadinia, Matineh Noei, Fatemeh Salehi · match Communications in Mathematical and in Computer Chemistry · 2022
For a graph G the Sombor index of G is defined as uv∈E(G) 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.