#
On Several Parameters of Super Line Graph ${\mathcal{L}}_{2}\left(G\right)$

^{*}

## Abstract

**:**

## 1. Introduction

**Theorem**

**1.**

## 2. Clique

**Lemma**

**1.**

**Theorem**

**2.**

**Theorem**

**3.**

**Proof.**

**Claim**

**1.**

**Proof.**

**Claim**

**2.**

**Proof.**

**Claim**

**3.**

**Proof.**

**Claim**

**4.**

**Proof.**

**Theorem**

**4.**

**Proof.**

**Claim**

**5.**

**Proof.**

**Claim**

**6.**

**Proof.**

**Claim**

**7.**

**Proof.**

## 3. Chromatic Number

**Theorem**

**5.**

**Proof.**

**Corollary**

**1.**

**Proof.**

**Corollary**

**2.**

**Proof.**

**Theorem**

**6.**

**Proof.**

**Proposition**

**1.**

**Proof.**

**Theorem**

**7.**

**Proof.**

## 4. Domination

**Theorem**

**8.**

**Proof.**

## 5. Discussion

**Problem**

**1.**

**Problem**

**2.**

**Problem**

**3.**

**Conjecture**

**1.**

**Conjecture**

**2.**

**Problem**

**4.**

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Graphs ${K}_{1,n-1}^{\prime}$ and ${K}_{1,n-1}+e$: (

**a**) ${K}_{1,n-1}^{\prime}$; (

**b**) ${K}_{1,n-1}+e$.

**Figure 2.**All unicyclic graphs of order 5, in which (

**a**), (

**b**) and (

**c**) have the cycle length three, and (

**d**) and (

**e**) have the cycle length four and five, respectively.

**Figure 3.**The labeling of edges of ${P}_{n}$ and ${\mathcal{L}}_{2}\left({P}_{n}\right)\left[D\right]$: (

**a**) ${P}_{n}$; (

**b**) the subgraph induced by D.

**Figure 4.**The labeling of edges of ${C}_{n}$ and ${\mathcal{L}}_{2}\left({C}_{n}\right)\left[D\right]$: (

**a**) ${C}_{n}$; (

**b**) subgraph of ${\mathcal{L}}_{2}\left({C}_{n}\right)$ induced by D.

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**MDPI and ACS Style**

Meng, J.; Wu, B.; Ma, H.
On Several Parameters of Super Line Graph *Axioms* **2023**, *12*, 276.
https://doi.org/10.3390/axioms12030276

**AMA Style**

Meng J, Wu B, Ma H.
On Several Parameters of Super Line Graph *Axioms*. 2023; 12(3):276.
https://doi.org/10.3390/axioms12030276

**Chicago/Turabian Style**

Meng, Jiawei, Baoyindureng Wu, and Hongliang Ma.
2023. "On Several Parameters of Super Line Graph *Axioms* 12, no. 3: 276.
https://doi.org/10.3390/axioms12030276