Incident Vertex Pi Coloring of Graph Families: Fan, Book, Gear, Windmill, Dutch Windmill and Crown Graph

In graph theory, the notion of graph coloring plays an important role and has several applications in the fields of science and engineering.Since the concept of map coloring was first proposed, many researchers have invented a wide range of graph coloring techniques, among which are vertex coloring, edge coloring, total coloring, perfect coloring, list coloring, acyclic coloring, strong coloring, radio coloring, and rank coloring, these are some of the important graph coloring methods that color the graph's vertices, edges, and regions with certain conditions.One of the coloring method is Incident Vertex PI coloring.This is a function of coloring from the set of pairs of incident vertices of every edge of a graph to the power set of colors.This method ensures that all vertices are properly colored, with an additional condition that ordered pair vertices for all edges of graph receive distinct colors.Many types of graphs are defined in the graph theory.In this paper, we have discussed the Incident Vertex PI Coloring numbers for the class of graph families, Fan graph, Book graph, Gear graph, Windmill graph, Dutch Windmill graph and Crown graph.