Geodesic
Partial ordering of trees and the classification of connected graphs and blocks
Diskretnaya Matematika, Tome 4 (1992) no. 2, pp. 66-73

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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)]. 
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     author = {G. I. Kalmykov},
     title = {Partial ordering of trees and the classification of connected graphs and blocks},
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G. I. Kalmykov. Partial ordering of trees and the classification of connected graphs and blocks. Diskretnaya Matematika, Tome 4 (1992) no. 2, pp. 66-73. http://geodesic.mathdoc.fr/item/DM_1992_4_2_a7/