Picture Fuzzy Incidence Graphs with Application

摘要

In this research article, we initiate the novel idea of picturefuzzy incidence graphs (PFIGs). We explain some innovative notionscomprising of picture fuzzy cut-vertices, picture fuzzy bridges, picturefuzzy incidence cutpairs, and picture fuzzy incidence cut-vertices. Somerudimentary theorems and essential results are also examined in the PFIGs.Further, we determine the different concepts together with the order, size,and certain kinds of degrees in PFIG. A new type of PFIGs namely,complete picture fuzzy incidence graphs (CPFIGs) and complement of(PFIGs) are also furnished. A comparative analysis of PFIGs with fuzzyincidence graphs is also presented. Finally, an application of PFIGs inthe control of illegal transportation of people from India to America isprovided.