# Bounds for the Generalized Distance Eigenvalues of a Graph

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Bounds on Generalized Distance Spectral Radius

**Lemma**

**1.**

**Theorem**

**1.**

**Proof.**

**Corollary**

**1.**

**Proof.**

**Corollary**

**2.**

**Proof.**

**Theorem**

**2.**

**Proof.**

**Remark**

**1.**

**Theorem**

**3.**

**Proof.**

**Remark**

**2.**

**Theorem**

**4.**

**Proof.**

**Example**

**1.**

## 3. Bounds for the k-th Generalized Distance Eigenvalue

**Lemma**

**2.**

**Theorem**

**5.**

**Proof.**

**Corollary**

**3.**

**Example**

**2.**

**Lemma**

**3.**

**Theorem**

**6.**

**Proof.**

**Theorem**

**7.**

**Theorem**

**8.**

**Proof.**

**Example**

**3.**

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Alhevaz, A.; Baghipur, M.; Ganie, H.A.; Shang, Y.
Bounds for the Generalized Distance Eigenvalues of a Graph. *Symmetry* **2019**, *11*, 1529.
https://doi.org/10.3390/sym11121529

**AMA Style**

Alhevaz A, Baghipur M, Ganie HA, Shang Y.
Bounds for the Generalized Distance Eigenvalues of a Graph. *Symmetry*. 2019; 11(12):1529.
https://doi.org/10.3390/sym11121529

**Chicago/Turabian Style**

Alhevaz, Abdollah, Maryam Baghipur, Hilal Ahmad Ganie, and Yilun Shang.
2019. "Bounds for the Generalized Distance Eigenvalues of a Graph" *Symmetry* 11, no. 12: 1529.
https://doi.org/10.3390/sym11121529