P3 CHROMATIC POLYNOMIALS OF DIFFERENT GRAPHS

Abstract

This thesis explores the P₃-chromatic polynomial, a crucial exten-sion of the classical chromatic polynomial in graph theory, aimed at examining path-based coloring constraints. The focus of the research is on identifying the P₃-chromatic polynomials for a range of graph fam-ilies, including cycle graphs, path graphs, ladder graphs, star graphs, and wheel graphs. Utilizing core principles of vertex coloring, chromatic numbers, and P₃-chromatic numbers, this work systematically calcu-lates the P₃-chromatic polynomials for these graph categories. The results obtained shed light on the structural properties of graphs under P₃-coloring conditions, thereby enhancing the theoretical framework of graph theory.