Jilin Daxue Xuebao (Gongxueban)/Journal of Jilin University (Engineering and Technology Edition) ISSN: 1671-5497 E-Publication: Online Open Access Vol: 43 Issue: 07-2024 DOI: 10.5281/zenodo.12703688 July 2024 | 62 OPTIMIZING GRAPH COLORING WITH BACTERIAL FORAGING OPTIMIZATION: EXPERIMENTAL INSIGHTS AND COMPUTATIONAL EFFICIENCY SHAINKY Research Scholar, Kalinga University, Raipur, Chhattisgarh. Email: shainky.dahiya.sd@gmail.com ASHA AMBHAIKAR Professor, Kalinga University, Raipur, Chhattisgarh. Email: asha.ambhaikar@kalingauniversity.ac.in Abstract The Graph Coloring Using Bacterial Foraging Optimization (BFO) algorithm efficiently addresses the graph coloring problem by ensuring adjacent nodes are assigned distinct colors. Utilizing BFO, we conducted experiments on graphs ranging from 10 to 100 nodes, demonstrating its effectiveness and scalability. Results show that the algorithm consistently achieved valid colorings with minimal chromatic numbers: 3 colors for 10 and 25 nodes, 6 colors for 50 and 75 nodes, and 7 colors for 100 nodes. Execution times were notably short, with the fastest at 0.004464 seconds for 10 nodes and 0.007576 seconds for 100 nodes. These findings underscore BFO's computational efficiency and suitability for graph coloring tasks across various graph sizes, suggesting its potential for broader applications in optimization and graph theory. Keywords: Graph Coloring, Bacterial Foraging Optimization (BFO), Nodes. 1. INTRODUCTION The Graph Coloring Problem is a captivating and extensively researched subject in the field of computer technology and discrete mathematics. Graph coloring is the process of assigning colors to the vertices of a graph in a manner that ensures no two adjacent vertices have the same color. This apparently uncomplicated operation has a plethora of practical uses, including addressing scheduling issues and optimizing resource allocation in compilers, managing frequency assignment in wireless networks, and solving Sudoku puzzles. The task at hand involves identifying the lowest number of colors required for a given graph, which is referred to as the graph's chromatic number. The Graph Coloring Problem, although having a clear definition, is widely known for its complexity and is categorized as NP-hard, which makes it a fertile field for studying algorithm design and computational theory (Wang et al.2024). Finding the chromatic number—that is, the fewest colors required to color a graph within the specified parameters—is a key objective in graph coloring. Theoretically fascinating as well as computationally demanding is this goal. Because no existing method can effectively solve every instance of the issue, it is categorized as NP-hard. Many heuristic and approximation algorithms have been developed as a result, as have precise techniques for particular graph classes (Kawakami et al. 2024). Numerous other fields in mathematics and computer science, including algorithm design, complexity theory, and combinatorial optimization, are intersected by the study of graph