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

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.

Estimation of most effected cycles and busiest network route based on complexity function of graph in fuzzy environment

“…All the data are taken from Mahapatra et al. ( 2021 ) and the website ( https://www.worldmeters.info/coronavirus/ ) dated 4th April, 2020. These five countries are USA, Spain, Italy, China, Germany which represents the vertices of the fuzzy graph of Fig.…”

“…of cases Mahapatra et al. ( 2021 ) Countries (vertices) Total cases Normalized score Membership value of vertices USA ( ) 258409 1 1 Spain ( ) 117710 0.46 0.46 Italy ( ) 119827 0.46 0.46 China ( ) 81620 0.32 0.32 Germany ( ) 89451 0.35 0.35 …”

Suggestion of Maintenance Criteria for Electric Railroad Facilities Based on Fuzzy TOPSIS

“…Pushpendra Kumar et al approached the predict liver disease problem using fuzzy sets and boosting techniques [12], and Yoosef B. Abushark et al conducted a usability evaluation study on security requirement perspective using the fuzzy AHP-TOPSIS approach [13]. Regarding COVID-19, Rupkumar Mahapatra et al conducted a study to distinguish COVID-19 detected regions by fuzzy directed graphs [14], M. Jayalakshmi et al…”

A Novel Description of Some Concepts in Interval-Valued Intuitionistic Fuzzy Graph with an Application

“…IFGs were first introduced by Atanassov [5] in 1999 and was further discussed in [6]. Mahapatra et al [7][8][9] explored concepts on fuzzy graphs. Rashmanlou and Pal [10,11] studied different kinds of FGs.…”