Open Access

ARTICLE

Colouring of COVID-19 Affected Region Based on Fuzzy Directed Graphs

by Rupkumar Mahapatra¹, Sovan Samanta², Madhumangal Pal¹, Jeong-Gon Lee^3,*, Shah Khalid Khan⁴, Usman Naseem⁵, Robin Singh Bhadoria⁶

1 Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India
2 Department of Mathematics, Tamralipta Mahavidyalaya, Tamluk, 721636, India
3 Division of Applied Mathematics, Wonkwang University, Iksan-Si, Jeonbuk, 54538, Korea
4 School of Engineering, RMIT University, Melbourne, 3001, Australia
5 School of Computer Science, University of Sydney Sydney, 2006, Australia
6 Department of Computer Science & Engineering, Birla Institute of Applied Sciences (BIAS), Bhimtal, Uttarakhand, 263136, India

* Corresponding Author: Jeong-Gon Lee. Email:

(This article belongs to the Special Issue: Recent Trends in Machine Intelligence respected to Medical Field Applications)

Computers, Materials & Continua 2021, 68(1), 1219-1233. https://doi.org/10.32604/cmc.2021.015590

Received 29 November 2020; Accepted 08 February 2021; Issue published 22 March 2021

Abstract

Graph colouring is the system of assigning a colour to each vertex of a graph. It is done in such a way that adjacent vertices do not have equal colour. It is fundamental in graph theory. It is often used to solve real-world problems like traffic light signalling, map colouring, scheduling, etc. Nowadays, social networks are prevalent systems in our life. Here, the users are considered as vertices, and their connections/interactions are taken as edges. Some users follow other popular users’ profiles in these networks, and some don’t, but those non-followers are connected directly to the popular profiles. That means, along with traditional relationship (information flowing), there is another relation among them. It depends on the domination of the relationship between the nodes. This type of situation can be modelled as a directed fuzzy graph. In the colouring of fuzzy graph theory, edge membership plays a vital role. Edge membership is a representation of flowing information between end nodes of the edge. Apart from the communication relationship, there may be some other factors like domination in relation. This influence of power is captured here. In this article, the colouring of directed fuzzy graphs is defined based on the influence of relationship. Along with this, the chromatic number and strong chromatic number are provided, and related properties are investigated. An application regarding COVID-19 infection is presented using the colouring of directed fuzzy graphs.

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