Decentralized federated learning (DFL) removes the server's single point of failure and communication bottleneck, offering a scalable alternative to centralized FL. Existing decentralized schemes typically use full‑neighborhood broadcasting, where each client sends its model update to all neighbors every round, incurring high communication cost and energy consumption. This paper proposes lightweight client selection methods based on spectral graph tools that exploit the spectral properties of the graph Laplacian on a fixed communication graph. By leveraging eigenvector embeddings and heat/diffusion kernel similarities, each client selects a subset of structurally relevant neighbors that most benefit convergence. The topology‑aware randomization matches or exceeds uniform neighborhood subsampling while approaching the accuracy of full broadcasting. On large, structurally rich graphs with strong data heterogeneity, the method gains about $3$ percentage points in accuracy and cuts the total number of transmitted messages by $50\%$ compared to naive broadcasting.\n\nReview: The study convincingly shows that graph‑spectral information can be harnessed to reduce communication overhead without sacrificing model performance, providing a practical direction for resource‑constrained decentralized learning.