Fuzzy Edge Chromatic Number of the Join of Fuzzy Graphs and Its Applications

Fuzzy edge coloring has proven to be a powerful tool for modeling and optimizing complex network systems, owing to its ability to effectively represent and manage the uncertainty in relational strengths and conflicts. It focuses on defining the fuzzy edge chromatic number, optimizing its computation, and exploring practical applications. For join graphs derived from fuzzy graphs, we propose an efficient fuzzy edge coloring algorithm and analyze the associated properties. Building on this, fuzzy edge coloring offers effective strategies for software promotion and traffic signal optimization. This work addresses fundamental theoretical challenges related to algorithm design, complexity analysis, and structural properties in fuzzy graph edge coloring, while also demonstrating its practical utility in complex scenarios such as software promotion and traffic signal optimization.