# General (α,2)-Path Sum-Connectivirty Indices of One Important Class of Polycyclic Aromatic Hydrocarbons

## Abstract

**:**

## 1. Introduction

#### 1.1. Application Background

#### 1.2. Definitions and Notations

## 2. Polycyclic Aromatic Hydrocarbons

## 3. Main Results on the General $(\mathit{\alpha},\mathbf{2})$-Path Sum-Connectivity Indices of ${\mathit{PAH}}_{\mathit{n}}$

**Theorem**

**1.**

**Proof**

**of**

**Theorem**

**1**

## 4. The Monotonicity and the Extremal Values of ${}^{\mathbf{2}}{\mathit{\chi}}_{\mathit{\alpha}}\left({\mathit{PAH}}_{\mathit{n}}\right)$

**Theorem**

**2.**

- For any real number α, we have ${}^{2}{\chi}_{\alpha}\left(PA{H}_{n}\right)$ is strictly increasing with respect to all positive integers n.
- The smallest general $(\alpha ,2)$-path sum-connectivity index of Polycyclic aromatic hydrocarbons is$${}^{2}{\chi}_{\alpha}{\left(PA{H}_{n}\right)}_{\mathrm{min}}{=}^{2}{\chi}_{\alpha}\left(PA{H}_{1}\right)=6[{9}^{\alpha}+2\xb7{7}^{\alpha}]$$

## 5. Conclusions

## 6. Further Research

## Funding

## Acknowledgments

## Conflicts of Interest

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Wang, H.
General (*α*,2)-Path Sum-Connectivirty Indices of One Important Class of Polycyclic Aromatic Hydrocarbons. *Symmetry* **2018**, *10*, 426.
https://doi.org/10.3390/sym10100426

**AMA Style**

Wang H.
General (*α*,2)-Path Sum-Connectivirty Indices of One Important Class of Polycyclic Aromatic Hydrocarbons. *Symmetry*. 2018; 10(10):426.
https://doi.org/10.3390/sym10100426

**Chicago/Turabian Style**

Wang, Haiying.
2018. "General (*α*,2)-Path Sum-Connectivirty Indices of One Important Class of Polycyclic Aromatic Hydrocarbons" *Symmetry* 10, no. 10: 426.
https://doi.org/10.3390/sym10100426