Computing dominant edge resolvability of graphs using the binary snow ablation optimizer

The graph metric known as dominant edge resolvability measures the ability to distinguish vertices of a graph through paths that include a selected set of edges. This study introduces a new approach for computing this metric using the Binary Snow Ablation Optimizer (BSAO), a meta-heuristic algorithm inspired by the snow ablation phenomenon. The problem is modeled as a binary optimization task, where each edge is represented by a binary variable, and a fitness function evaluates the uniqueness of vertex identification. BSAO is then employed to efficiently explore the solution space and approximate optimal solutions. Experimental results on diverse graphs show that the proposed method outperforms existing techniques in both computational efficiency and solution quality, while maintaining scalability to large-scale graphs, making it a practical tool for real-world applications.