On Sombor Index

Kinkar Chandra Das,Yilun Shang,Ismail Naci Cangul,Ahmet Sinan Çevik

doi:10.3390/sym13010140

On Sombor Index

Kinkar Chandra Das, Yilun Shang + Show 2 more

Open Access

https://doi.org/10.3390/sym13010140

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Abstract

The concept of Sombor index (SO) was recently introduced by Gutman in the chemical graph theory. It is a vertex-degree-based topological index and is denoted by Sombor index SO: SO=SO(G)=∑vivj∈E(G)dG(vi)2+dG(vj)2, where dG(vi) is the degree of vertex vi in G. Here, we present novel lower and upper bounds on the Sombor index of graphs by using some graph parameters. Moreover, we obtain several relations on Sombor index with the first and second Zagreb indices of graphs. Finally, we give some conclusions and propose future work.

Highlights

Gutman presented a novel approach to the vertexdegree-based topological index of graphs
We present a relation between Sombor index SO( G ) and the second Zagreb index
Many topological indices have been defined in the literature and several of them have found applications as a means to model physical, chemical, pharmaceutical, and other properties of molecules

Summary

Introduction

In the mathematical and chemical literature, several dozens of vertex-degree-based graph invariants (usually referred to as “topological indices”) have been introduced and extensively studied. Their general formula is ms in published maps and institutio-. Gutman presented a novel approach to the vertexdegree-based topological index of (molecular) graphs. For this we need the following definition: Definition 1 ([28]). The number of vertices in the largest independent set is called the independence number of a given graph, which is denoted conventionally by α.

Bounds on Sombor Index of Graphs

Relation between Sombor Index with Zagreb Indices of Graphs

Conclusions