Optimizing Edge Coloring in Undirected Graphs Using Incidence Matrix

Graph edge coloring is a fundamental problem in combinations optimization with applications in various domains. This paper presents an algorithm for efficiently edge coloring of undirected graphs using a stack-based approach and an incidence matrix. The algorithm initializes a stack with a unique color for each edge, starting the traversal from a specified vertex. Coloring is performed by considering the top most color of the stack, ensuring that adjacent edges do not share the same color. The algorithm employs a horizontal traversal in the incidence matrix and back tracking strategies to handle conflicts. The proposed method is evaluated through extensive experimentation on diverse graph types, revealing insights into its performance, strengths, and limitations. The analysis includes considerations of parameter sensitivity, optimization impact, back tracking behavior, and scalability. The results offer valuable guidance for understanding the algorithm’s applicability in different scenarios and provide a foundation for further refinements and optimizations. The algorithm demonstrates effectiveness in preserving graph structure and optimizing the allocation of colors, providing a valuable tool for various applications such as scheduling, network optimization, and resource allocation. Theoretical analyses and experimental results showcase the algorithm’s efficiency and applicability across diverse graph structures, establishing it as a practical solution for edge coloring in undirected graphs represented by incidence matrices.