On the Graphs with Minimum Sombor Index

Aarman Aashtab, Saieed Akbari, Saba Madadinia, Matineh Noei, Fatemeh Salehi

2022match Communications in Mathematical and in Computer Chemistry19 citationsDOI

Abstract

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.

Topics & Concepts

Index (typography)MathematicsCombinatoricsStatisticsComputer scienceProgramming languageGraph Labeling and Dimension ProblemsGraph theory and applicationsAdvanced Graph Theory Research