objective function for graph coloring with ORtools solver

Question

i wrote a cp function to solve graph coloring with ORtools

(minimizing color usage, when the colors of every two vertices on an edge needs to be different) i get weird result,which isnt optimal, and im not sure why- i think my objective function is wrong, or my constraint formulation,any help? thanks

    def cp_with_ortools(node_count, edge_count, edges, M, solution, max_degree):
        global colors
        from ortools.sat.python import cp_model
        solution = [0] * (node_count)# list of colors to nodes initialized with 0
        # Creates the model.
        model = cp_model.CpModel()

        # Creates the variables.
        for i in range(node_count):
            solution[i] = model.NewIntVar(0, int(node_count), '')
            #shouldnt be max_degree? isnt working..
            
        # Adds  constraint
        for edge in edges:
            model.Add(solution[edge[0]] != solution[edge[1]])

        # Create the objective function
        obj_var = model.NewIntVar(0, node_count, 'makespan')
        model.AddMaxEquality(obj_var,solution)
        model.Minimize(obj_var)

        #model.Minimize(len(set(solution)))
        #model.Minimize(sum(solution)))

        # Creates a solver and solves the model.
        solver = cp_model.CpSolver()

        status = solver.Solve(model)

        if status == cp_model.OPTIMAL:
            colors = [solver.Value(solution[i]) for i in range(node_count)]

        return colors