The Minimum Vertex Cover (MVC) problem is a fundamental NP-complete problem in graph theory that seeks the smallest set of vertices covering all edges in an undirected graph G = (V, E). This paper presents the find_vertex_cover algorithm, an innovative approximation method that transforms the problem to maximum degree-1 instances via auxiliary vertices. The algorithm computes solutions using weighted dominating sets and vertex covers on reduced graphs, enhanced by ensemble heuristics including maximum-degree greed…