Applications of graph theory and group theory in chemistry, physics

The work is devoted to the consideration of applications of mathematics, in particular, graph theory and group theory in chemistry and physics. Chemistry was one of the first to adopt the ideas of graph theory. Mathematical chemistry is a section of theoretical chemistry that studies the application of mathematics to chemical problems. The possibility of formalizing molecules in the language of structural chemistry using graphs allows one to determine the number of different isomers using graph theory methods. The main tool in mathematical chemistry is mathematical modeling using computer technology. The methods of graph theory are actively used in three areas of chemistry: structural chemistry, chemical kinetics, and chemical physics of polymers. Group theory has found application in many areas of physics. Group theory serves to explain the most important characteristics of atomic spectra. Group theory provides an opportunity for a uniform approach to a large number of problems in solid state physics. Matrix groups and unitary group representations are actively used in these studies. Irreducible group representations are used to classify vibrational and electronic states of a crystal. Methods of group theory are applied to models of problems of classifying electronic states of a crystal. In crystallography, much attention is paid to applications of group theory methods to the study of vibrations of atoms that make up a molecule relative to their equilibrium positions. The results can be useful in encoding information in space communications sessions.