A study of plithogenic graphs: applications in spreading coronavirus disease (COVID-19) globally

Abstract

During the last two decades, the world has experienced three major outbreaks of Coronaviruses, namely severe acute respiratory syndrome (SARS- CoV), middle east respiratory syndrome (MERS-CoV), and the current ongoing pandemic of severe acute respiratory syndrome 2 (SARS-CoV-2). The SARS-CoV-2 caused the disease known as Coronavirus Disease 2019 (COVID-19). Since its discovery for the first time in Wuhan, China, in December 2019, the disease has spread very fast, and cases have been reported in more than 200 countries/territories. In this study, the idea of Smarandache's pathogenic set is used to discuss the novel COVID-19 spread. We first introduced plithogenic graphs and their subclass, like plithogenic fuzzy graphs. We also established certain binary operations like union, join, Cartesian product, and composition of pathogenic fuzzy graphs, which are helpful when we discuss combining two different graphs. In the end, we investigate the spreading trend of COVID-19 by applying the pathogenic fuzzy graphs. We observe that COVID-19 is much dangerous than (MERS-CoV) and (SARS-CoV). Moreover, as the SARS-CoV and MERS-CoV outbreaks were controlled, there are greater chances to overcome the current pandemic of COVID-19 too. Our model suggests that all the countries should stop all types of traveling/movement across the borders and internally too to control the spread of COVID-19. The proposed model also predicts that in case precautionary measures have not been taken then there is a chance of severe outbreak in future.

Keywords: Graphs; Plithogenic graphs; Plithogenic sets.

Fig. 1

a A plithogenic fuzzy graph ${\mathrm{P}}_{\mathrm{F}}\mathrm{G}$. b) A fuzzy graph

Fig. 2

A plithogenic fuzzy graph ${\mathrm{P}}_{\mathrm{FG}1}$

Fig. 3

A plithogenic fuzzy graph ${\mathrm{P}}_{\mathrm{FG}2}$

Fig. 4

aUnion of two plithogenic fuzzy graphs P_FG1UFG2. b Union of two fuzzy graphs

Fig. 5

Plithogenic fuzzy graph P_FG1

Fig. 6

Plithogenic fuzzy graph P_FG2

Fig. 7

a Join of plithogenic fuzzy graphs P_FG1+FG2. b Join of two fuzzy graphs

Fig. 8

Plithogenic fuzzy graph P_FG1

Fig. 9

A plithogenic fuzzy graph P_FG2

Fig. 10

Cartesian product of two plithogenic graphs

Fig. 11

Composition of two plithogenic fuzzy graphs

Fig. 12

a A plithogenic graph showing effects of diffrent CoVs. b A fuzzy graph showing effects of different CoVs. c An intuitionistic fuzzy graph showing effects of different CoVs. d A nutrosophic graph showing effects of different CoVs

Fig. 13

a Plithogenic graph showing spreading of COVID-19. b Fuzzy graph showing spreading of COVID-19. c A intuitionistic fuzzy graph showing spreading of COVID-19. d A neutrosophic graph showing spreading of COVID-19