On the enumeration of phase diagrams

The topological isomorphism of polyhedra with trivalent vertices and solid-liquid diagrams of three-component systems allows the problem of constructing the complete set of the topological types of diagrams with a given set of characteristics to be reduced to the problem of the generation of marked cubic graphs, which are the Schlegel projections of polyhedra. The problem of the enumeration of possible topological types of melting diagrams containing M binary and N ternary stoichiometric congruently melting compounds is considered. Relations between the topological characteristics of such diagrams are given. The total number of topologically different types of melting diagrams with one binary and one ternary congruently melting compounds was found to be 64.