# General Multiplicative Zagreb Indices of Graphs with a Small Number of Cycles

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## Abstract

**:**

## 1. Introduction

## 2. Preliminary Results

**Lemma**

**1.**

**Proof.**

**Corollary**

**1.**

**Proof.**

**Corollary**

**2.**

**Proof.**

## 3. Bicyclic Graphs with Given Number of Pendant Vertices

**Theorem**

**1.**

**Proof.**

**Example**

**1.**

**Theorem**

**2.**

**Proof.**

**Example**

**2.**

## 4. Graphs with Given Number of Pendant Vertices and Small Number of Edges

**Theorem**

**3.**

**Proof.**

**Example**

**3.**

**Theorem**

**4.**

**Proof.**

**Theorem**

**5.**

**Example**

**4.**

**Theorem**

**6.**

**Proof.**

**Theorem**

**7.**

**Theorem**

**8.**

**Example**

**5.**

## 5. Bounds for $\mathit{a}<\mathbf{0}$

**Lemma**

**2.**

**Theorem**

**9.**

**Theorem**

**10.**

**Theorem**

**11.**

**Theorem**

**12.**

**Theorem**

**13.**

**Theorem**

**14.**

**Theorem**

**15.**

**Theorem**

**16.**

## 6. Conclusion

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Alfuraidan, M.R.; Vetrík, T.; Balachandran, S.
General Multiplicative Zagreb Indices of Graphs with a Small Number of Cycles. *Symmetry* **2020**, *12*, 514.
https://doi.org/10.3390/sym12040514

**AMA Style**

Alfuraidan MR, Vetrík T, Balachandran S.
General Multiplicative Zagreb Indices of Graphs with a Small Number of Cycles. *Symmetry*. 2020; 12(4):514.
https://doi.org/10.3390/sym12040514

**Chicago/Turabian Style**

Alfuraidan, Monther R., Tomáš Vetrík, and Selvaraj Balachandran.
2020. "General Multiplicative Zagreb Indices of Graphs with a Small Number of Cycles" *Symmetry* 12, no. 4: 514.
https://doi.org/10.3390/sym12040514