Payame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31309120240501A Hybrid Floyd-Warshall and Graph Coloring Algorithm for Finding the Smallest Number of Colors Needed for a Distance Coloring of Graphs1851941062610.30473/coam.2023.68880.1244ENHanifaMosawiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran.0000-0001-8960-588XMostafaTavakolliDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran.0000-0002-3315-1759KhatereGhorbani-MoghadamMosaheb Institute of Mathematics, Kharazmi University, Tehran, Iran.0000-0003-0109-6406Journal Article20230826Graph coloring is a crucial area of research in graph theory, with numerous algorithms proposed for various types of graph coloring, particularly graph p-distance coloring. In this study, we employ a recently introduced graph coloring algorithm to develop a hybrid algorithm approximating the chromatic number p-distance, where $p$ represents a positive integer number. We apply our algorithm to molecular graphs as practical applications of our findings.https://mathco.journals.pnu.ac.ir/article_10626_1d3b0b6b1881cfc48c06bf561ecafcc0.pdf