Decomposing Johnson Graphs for Dynamic Frequency Allocation in 5G Networks

Optimal bandwidth utilization and interference-free frequency allocation in 5G networks continue to be major challenges. This paper presents a new method for dynamic frequency management based on Johnson graph decomposition. The Johnson graph <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{J}(\mathbf{n}, \mathbf{k})$</tex> allows for interference-free allocation since its edges indicate shared elements and its vertices represent frequency subsets. By working in parallel levels and minimizing interference between nearby cells, the decomposition framework guarantees seamless handoffs in crowded metropolitan locations. Independent frequency clusters are found by combining spectral graph and modular decomposition approaches to optimize reuse with the least amount of overlap. Adaptive dynamic rearrangement of spectrum allocations model in response to environmental factors, user demand, and traffic. Johnson graph decomposition is a powerful method that is suitable for real-world 5G situations, and simulation shows improved spectrum use, lower latency, enhanced 5G network performance, and adjusts to the changing needs of next-generation wireless networks due to its effectiveness and scalability.