# General Randić Index of Unicyclic Graphs and Its Applications to Drugs

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Unicyclic Graphs with Maximum General Randić Index

**Lemma 1.**

**Proof.**

- (i)
- If $a=b=1$, then

- (ii)
- If $a\ge 2$ and $b=1$, then

- (iii)
- If $a,b\ge 2$, then

**Lemma 2.**

**Proof.**

**Theorem 1.**

**Proof.**

**Theorem 2.**

**Proof.**

**Problem 1.**

**Problem 2.**

**Problem 3.**

## 3. QSPR/QSAR of Randić Index

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Table 1.**Correlation of ${R}_{-1}\left(G\right)$ with bp, mv, mr, hv, and st for chemical graphs up to order $7$.

${\mathit{R}}_{-1}\left(\mathit{G}\right)$ vs. bp | ${\mathit{R}}_{-1}\left(\mathit{G}\right)$ vs. mv | ${\mathit{R}}_{-1}\left(\mathit{G}\right)$ vs. mr | ${\mathit{R}}_{-1}\left(\mathit{G}\right)$ vs. hv | ${\mathit{R}}_{-1}\left(\mathit{G}\right)$ vs. st |
---|---|---|---|---|

0.976893697 | 0.947992593 | 0.952529194 | 0.987125973 | 0.893037379 |

**Table 2.**Correlation of ${R}_{-1}\left(G\right)$ with bp, mv, mr, hv, and st for chemical graphs up to order $7$.

${\mathit{R}}_{-1}\left(\mathit{G}\right)$ vs. bp | ${\mathit{R}}_{-1}\left(\mathit{G}\right)$ vs. mv | ${\mathit{R}}_{-1}\left(\mathit{G}\right)$ vs. mr | ${\mathit{R}}_{-1}\left(\mathit{G}\right)$ vs. hv | ${\mathit{R}}_{-1}\left(\mathit{G}\right)$ vs. st |
---|---|---|---|---|

0.9543 | 0.8987 | 0.9073 | 0.9744 | 0.8307 |

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Altassan, A.; Imran, M.
General Randić Index of Unicyclic Graphs and Its Applications to Drugs. *Symmetry* **2024**, *16*, 113.
https://doi.org/10.3390/sym16010113

**AMA Style**

Altassan A, Imran M.
General Randić Index of Unicyclic Graphs and Its Applications to Drugs. *Symmetry*. 2024; 16(1):113.
https://doi.org/10.3390/sym16010113

**Chicago/Turabian Style**

Altassan, Alaa, and Muhammad Imran.
2024. "General Randić Index of Unicyclic Graphs and Its Applications to Drugs" *Symmetry* 16, no. 1: 113.
https://doi.org/10.3390/sym16010113