# On Sombor Index

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## Abstract

**:**

## 1. Introduction

**Definition**

**1**

## 2. Bounds on Sombor Index of Graphs

**Lemma**

**1.**

- (i)
- $SO\left(G\right)>SO(G-e)$, where $e={v}_{i}{v}_{j}$ is any edge in G,
- (ii)
- $SO(G+e)>SO\left(G\right)$, where $e={v}_{i}{v}_{j}$ and vertices ${v}_{i}$ & ${v}_{j}$ are non-adjacent in G.

**Theorem**

**1.**

**Proof.**

**Corollary**

**1**

**Theorem**

**2.**

**Proof.**

**Theorem**

**3.**

**Proof.**

**Theorem**

**4.**

**Proof.**

**Theorem**

**5.**

**Proof.**

**Theorem**

**6.**

**Proof.**

## 3. Relation between Sombor Index with Zagreb Indices of Graphs

**Lemma**

**2.**

**Theorem**

**7.**

**Proof.**

**Theorem**

**8.**

**Proof.**

**Lemma**

**3.**

**Theorem**

**9.**

**Proof.**

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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Das, K.C.; Çevik, A.S.; Cangul, I.N.; Shang, Y.
On Sombor Index. *Symmetry* **2021**, *13*, 140.
https://doi.org/10.3390/sym13010140

**AMA Style**

Das KC, Çevik AS, Cangul IN, Shang Y.
On Sombor Index. *Symmetry*. 2021; 13(1):140.
https://doi.org/10.3390/sym13010140

**Chicago/Turabian Style**

Das, Kinkar Chandra, Ahmet Sinan Çevik, Ismail Naci Cangul, and Yilun Shang.
2021. "On Sombor Index" *Symmetry* 13, no. 1: 140.
https://doi.org/10.3390/sym13010140