Moplex orderings generated by the LexDFS algorithm

Let G be a graph with vertex set V. A moplex of G is both a clique and a module whose neighborhood is a minimal separator in G or empty. A moplex ordering of G is an ordered partition (X"1,X"2,...,X"k) of V for some integer k into moplexes which are defined in the successive transitory elimination graphs, i.e., for 1=