Аннотация:In the article, at the mathematical level of rigor, it is shown that the pair of concepts ”covalence — mesoionicity” correlates in the same way as the pair ”kekuleness — non-kekuleness”. A criterion for a structure to be mesoionic (mesoionicity criterion) is formulated and proved, which makes it possible to enumerate all mono-charged mesoionic structures (mesomeric betaines) on a given graph. The mesoionicity criterion and the Kasteleyn theorem (on counting thenumber of perfect matchings in a graph) were used as the basis for a computer program that classifies dipolar resonance structures. The work of the program is demonstrated on the lists of obtained mesoionic structures. A general approach to mesoionicity is discussed
