On general Sombor index

TL;DR

This paper investigates bounds and relationships of the general Sombor index, a graph invariant that unifies the forgotten and Sombor indices, and explores its extremal properties and connections to other indices.

Contribution

It introduces bounds for the general Sombor index based on graph parameters and examines its relations with other generalized indices, extending existing graph theory knowledge.

Findings

Derived bounds for the general Sombor index using graph parameters

Established Nordhaus-Gaddum-type results for the index

Explored relations with the general Randić and sum-connectivity indices

Abstract

We present the bounds in terms of other important graph parameters for general Sombor index which generalises both the forgotten index and the Sombor index. We also explore the Nordhaus-Gaddum-type result for the general Sombor index. We present further the relations between general Sombor index and other generalised indices: general Randi\'c index and general sum-connectivity index.