# A Study on Domination in Vague Incidence Graph and Its Application in Medical Sciences

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

**Definition**

**4.**

**Example**

**1.**

**Definition**

**5.**

**Definition**

**6.**

## 3. Vague Incidence Graph

**Definition**

**7.**

**Example**

**2.**

**Definition**

**8.**

**Definition**

**9.**

**Definition**

**10.**

**Definition**

**11.**

**Example**

**3.**

**Example**

**4.**

**Definition**

**12.**

**Definition**

**13.**

**Definition**

**14.**

**Example**

**6.**

**Definition**

**15.**

**Example**

**7.**

**Definition**

**16.**

**Definition**

**17.**

**Definition**

**18.**

**Example**

**8.**

**Theorem**

**1.**

**Proof.**

**Definition**

**19.**

**Example**

**9.**

**Definition**

**20.**

**Example**

**10.**

**Theorem**

**2.**

**Proof.**

**Definition**

**21.**

**Example**

**11.**

**Theorem**

**3.**

**Proof.**

**Corollary**

**1.**

**Proof.**

**Definition**

**22.**

**Example**

**12.**

**Definition**

**23.**

**Definition**

**24.**

**Definition**

**25.**

**Example**

**13.**

**Theorem**

**4.**

**Proof.**

**Theorem**

**5.**

**Proof.**

**Theorem**

**6.**

**Proof.**

## 4. Application of VIDS for COVID-19 Testing Facility

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Notation | Meaning |
---|---|

$\zeta $ | Vague Incidence Graph |

FG | Fuzzy Graph |

VG | Vague Graph |

FIG | Fuzzy incidence Graph |

VIG | Vague Incidence Graph |

DS | Dominating Set |

VS | Vague Set |

VIDS | Vague Incidence Dominating Set |

VIIS | Vague Incidence Irredundant Set |

VDS | Vague Dominating Set |

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**MDPI and ACS Style**

Rao, Y.; Kosari, S.; Shao, Z.; Cai, R.; Xinyue, L.
A Study on Domination in Vague Incidence Graph and Its Application in Medical Sciences. *Symmetry* **2020**, *12*, 1885.
https://doi.org/10.3390/sym12111885

**AMA Style**

Rao Y, Kosari S, Shao Z, Cai R, Xinyue L.
A Study on Domination in Vague Incidence Graph and Its Application in Medical Sciences. *Symmetry*. 2020; 12(11):1885.
https://doi.org/10.3390/sym12111885

**Chicago/Turabian Style**

Rao, Yongsheng, Saeed Kosari, Zehui Shao, Ruiqi Cai, and Liu Xinyue.
2020. "A Study on Domination in Vague Incidence Graph and Its Application in Medical Sciences" *Symmetry* 12, no. 11: 1885.
https://doi.org/10.3390/sym12111885