Graph theory and algebraic topology in the study of phase diagrams of multi-component condensed systems

Based on a constructive generalization of the results of works on the topology of phase diagrams of multi-component condensed systems, the contribution of these studies to the general theory of phase diagrams is presented. General fundamental specific features characteristic of certain classes of diagrams were identified as a result of the systematic study of this topology. The topology of subsolidus isobaric-isothermal phase diagrams, as well as melting diagrams, is considered. This review can be useful for the formulation and solution of new problems in the study of phase diagrams of multi-component systems.