### Journals Information

**
Mathematics and Statistics Vol. 12(4), pp. 366 - 373 DOI: 10.13189/ms.2024.120408 Reprint (PDF) (1304Kb) **

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

**Sunil B. Thakare ^{1}, Archana Bhange ^{2}, H. R. Bhapkar ^{3}^{,*}**

^{1}Department of Mathematics, MIT School of Engineering and Sciences, MIT Art, Design and Technology University, India

^{2}Department of Mathematics, MANET, MIT Art, Design and Technology University, India

^{3}Department of Mathematics, Central University of Kashmir, Ministry of Education, Government of India, India

**ABSTRACT**

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.

**KEYWORDS**

Incident Vertex PI Coloring, Fan Graph, Book Graph, Windmill Graph, Dutch Windmill Graph, Gear Graph and Crown Graph

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Sunil B. Thakare , Archana Bhange , H. R. Bhapkar , "Incident Vertex Pi Coloring of Graph Families: Fan, Book, Gear, Windmill, Dutch Windmill and Crown Graph," Mathematics and Statistics, Vol. 12, No. 4, pp. 366 - 373, 2024. DOI: 10.13189/ms.2024.120408.

(b). APA Format:

Sunil B. Thakare , Archana Bhange , H. R. Bhapkar (2024). Incident Vertex Pi Coloring of Graph Families: Fan, Book, Gear, Windmill, Dutch Windmill and Crown Graph. Mathematics and Statistics, 12(4), 366 - 373. DOI: 10.13189/ms.2024.120408.