Efficient and Robust Graph Coloring Algorithm for Graph Coloring Problem: Malatya Vertex Coloring Algorithm

Abstract

The graph coloring problem involves coloring the nodes of a graph using the minimum number of colors such that no two adjacent nodes share the same color. This NP-hard problem has various real-world applications, including scheduling problems, map coloring, and resource allocation. Although numerous algorithms have been proposed in the literature to solve this problem, there is a lack of effective and robust algorithms that perform well across different types of graphs. In this study, we propose the Malatya Vertex Coloring Algorithm, an efficient and robust solution for the graph coloring problem. The proposed algorithm calculates the Malatya centrality value for each node by summing the ratios of the node’s degree to the degrees of its neighboring nodes. Starting from the node with the highest Malatya centrality value, the graph is colored such that each node is assigned a color different from its neighbors. The effectiveness of the proposed algorithm is demonstrated through extensive testing and analysis. First, experiments were conducted on benchmark graphs from the literature, varying in size and complexity based on the number of nodes and edges. Additionally, tests were performed on social network graphs (which model social connections and behaviors) as well as randomly generated graphs with different densities and sizes. The results show that the proposed algorithm outperforms well-known existing methods such as Welsh-Powell, Greedy Coloring, DSatur, and RLF in terms of efficiency, robustness, and success rate. Moreover, in some graph types, it yields better results than MSISCA, another efficient and robust algorithm. It is mathematically proven that the proposed algorithm provides a solution in polynomial time for any arbitrary graph and guarantees an optimal solution for specific graph classes. The analyses and experimental results demonstrate that the Malatya Vertex Coloring Algorithm delivers effective and robust solutions for the graph coloring problem across various graph types without any constraints or parameter dependencies.