On relations between Sombor and other degree-based indices

Abstract

Recently, a novel topological invariant based on degrees of end-vertices of an edge in a graph was put forward. It was named Sombor index. The definition of the Sombor invariant suggests another, rather a geometric view onto graph edges. Here, the mathematical relations between the Sombor index and some other well-known degree-based descriptors are investigated. Then, a few results of Nordhaus–Gaddum-type are obtained. Finally, computational testing and comparison with other well-established indices are presented.