Colouring of COVID-19 Affected Region Based on Fuzzy Directed Graphs
Rupkumar Mahapatra, Sovan Samanta, Madhumangal Pal, Jeong-Gon Lee, Shah Khalid Khan, Usman Naseem, Robin Singh Bhadoria
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.