Graph Coloring Problem in Graph Theory Research with MATLAB Implementation

This MATLAB program provides a comprehensive solution for the graph coloring problem in graph theory, offering high efficiency and exceptional user-friendliness. The implementation includes multiple graph coloring algorithms such as greedy coloring, Welsh-Powell algorithm, and DSATUR (Degree of Saturation) heuristic, allowing users to select the most appropriate method for their specific graph structures. The program features an intuitive interface where users can input graph data through adjacency matrices or edge lists. Key functions include graph visualization capabilities, color assignment optimization, and chromatic number calculation. Users can customize parameters like color selection strategies and optimization thresholds to tailor the solution to their research requirements. The code architecture supports both vertex coloring and edge coloring problems, with built-in validation checks for proper coloring conditions. The program includes detailed documentation covering algorithm implementations, complexity analysis, and usage examples. Support resources provide guidance on handling various graph types including planar graphs, bipartite graphs, and random graphs. This MATLAB implementation serves as an excellent resource for graph theory researchers and students, offering robust tools for solving coloring problems while maintaining code modularity for future extensions and algorithm comparisons.