# Domination in Join of Fuzzy Incidence Graphs Using Strong Pairs with Application in Trading System of Different Countries

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## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

**Definition**

**1**

**Definition**

**2**

**Definition**

**3**

**Example**

**1.**

**Definition**

**4**

**Definition**

**5**

**Definition**

**6**

**Definition**

**7**

**Definition**

**8**

**Definition**

**9**

**Definition**

**10**

**Definition**

**11**

**Definition**

**12**

## 3. Domination in Fuzzy Incidence Graph Using Strong Pair

**Definition**

**13.**

**Definition**

**14.**

**Definition**

**15.**

**Definition**

**16.**

**Definition**

**17.**

**Example**

**2.**

**Definition**

**18.**

**Example**

**3.**

**Definition**

**19.**

**Definition**

**20.**

**Definition**

**21.**

**Definition**

**22.**

**Example**

**4.**

**Theorem**

**1.**

**Proof.**

**Example**

**5.**

**Definition**

**23.**

**Theorem**

**2.**

**Proof.**

**Example**

**6.**

**Theorem**

**3.**

**Proof.**

**Example**

**7.**

**Theorem**

**4.**

**Proof.**

**Example**

**8.**

**Theorem**

**5.**

**Proof.**

**Example**

**9.**

## 4. Domination in the Join of Fuzzy Incidence Graphs

**Definition**

**24.**

**Definition**

**25.**

**Theorem**

**6.**

**Proof.**

**Theorem**

**7.**

**Proof.**

**Example**

**10.**

## 5. Accurate Domination in Fuzzy Incidence Graphs

**Definition**

**26.**

**Definition**

**27.**

**Example**

**11.**

**Theorem**

**8.**

**Proof.**

**Theorem**

**9.**

**Proof.**

**Theorem**

**10.**

**Proof.**

## 6. Real-Life Application of Strong Pair Domination Number

## 7. Comparative Analysis

## 8. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 8.**SFIG ${\widehat{G}}_{e}\oplus {\widehat{G}}_{f}$ with $M[{\gamma}_{s}({\widehat{G}}_{e}\oplus {\widehat{G}}_{f})]=1$.

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**MDPI and ACS Style**

Nazeer, I.; Rashid, T.; Hussain, M.T.; Guirao, J.L.G. Domination in Join of Fuzzy Incidence Graphs Using Strong Pairs with Application in Trading System of Different Countries. *Symmetry* **2021**, *13*, 1279.
https://doi.org/10.3390/sym13071279

**AMA Style**

Nazeer I, Rashid T, Hussain MT, Guirao JLG. Domination in Join of Fuzzy Incidence Graphs Using Strong Pairs with Application in Trading System of Different Countries. *Symmetry*. 2021; 13(7):1279.
https://doi.org/10.3390/sym13071279

**Chicago/Turabian Style**

Nazeer, Irfan, Tabasam Rashid, Muhammad Tanveer Hussain, and Juan Luis García Guirao. 2021. "Domination in Join of Fuzzy Incidence Graphs Using Strong Pairs with Application in Trading System of Different Countries" *Symmetry* 13, no. 7: 1279.
https://doi.org/10.3390/sym13071279