A study on fuzzy incidence coloring of graphs

Abstract

The present research deals with the new type of coloring in fuzzy newlinegraph theory known as Fuzzy Incidence Coloring. Fuzzy Incidence Coloring newlineis defined, and some of its equivalent conditions required for a fuzzy graph to newlineapply Fuzzy Incidence Coloring have been discussed in the study. Moreover, newlinea Fuzzy Incidence Coloring Number is defined, and bounds for various Fuzzy newlineIncidence Graphs are derived. An algorithm for performing Fuzzy Incidence newlineColoring on any fuzzy network has been developed. Also a ,C++ program has newlinebeen developed to perform Fuzzy Incidence Coloring on a Fuzzy Incidence newlinecycle graph for any number of vertices. newlineThe fundamental operations such as union, intersection, join, and newlinethe cartesian product between any two Fuzzy Incidence Graphs and a newlinecomplement of a Fuzzy Incidence Graph are introduced. Additionally, for newlinecertain Fuzzy Incidence Graphs, the bounds of Fuzzy Incidence Coloring newlineNumber using Fuzzy Incidence Coloring are depicted. newlineFinally, the Fuzzy Incidence algorithm has been applied to two newlinesignificant real-time problems to reduce tragic incidents. Fuzzy Incidence newlineColoring has been used to test a traffic flow problem with eight vertices in newlinewhich a few vehicles in some incidences must wait while vehicles in adjacent newlineincidences pass, thereby reducing the vehicles waiting time. The study newlineattempts to investigate missing persons data in India, in order to predict the newlinerisk of human trafficking in the year 2021. Using Fuzzy Incidence Coloring, a newlinerigorous assessment of the cases of missing victims is carried out in various newlineiv newlineparts of Maharashtra in order to rescue the victims from traffickers as quick as newlinepossible without incurring any loss. Fuzzy Incidence Coloring provides a newlinemore effective solution to traffic flow issues as well as for human trafficking newline