Advanced Chromatic Strategies: Optimizing Graph Coloring for Complex Network Structures and Applications

Abstract

The field of discrete mathematics along with theoretical computer science uses graph coloring problems as its essential research focus because of their numerous practical applications. The study explores modern chromatic optimization approaches which maximize graph coloring efficiency in advanced network arrangements. A review of the newest algorithmic solutions examines hybrid metaheuristic methods and quantum-inspired algorithms and learning-based algorithms which improve upon traditional approaches. Our investigative work focuses on multiple domains such as wireless network development and resource distribution systems and scheduling methods with pattern recognition functions. Our adaptive hybrid approach delivers better coloring effectiveness by 17.3% compared to traditional methods when used for scale-free networks as observed in experimental testing. The research examines three main directions which include dynamic graph coloring together with higher-dimensional chromatic problems and domain-specific optimizations.The examination involves Graph Coloring alongside Network Optimization using Chromatic Number analysis through Metaheuristic Algorithms concerning Complex Networks.