Partial ordering of trees and the classification of connected graphs and blocks

The article consists of two parts. In the first part, partial ordering of trees and the notion of the spanning tree of a connected graph are introduced, and, on the basis of the last one, a classification of connected graphs is given. In the second part, the notion of spanning tree of a block is introduced and, on its basis, a classification of blocks is given. The obtained results have applications to statistical mechanics. Most of them have been announced in the recent article of the author [Teor. Mat. Fiz. 84, No. 2, 279–289 (1990)].