Geodesic
The second Riddel relation and its consequences
Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 1, pp. 20-32

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The second Riddell relation relates the generating functions for the number of labeled connected graphs and the number of labeled blocks. We consider the conditions under which this relation is true for a subclass of connected graphs. Under these conditions, the formulas are valid that express the number of graphs from a subclass of labeled connected graphs trough the generating function of their blocks. By way of application, we obtain expressions for the numbers of labeled connected and 2-connected series-parallel graphs. Bibliogr. 22.
Keywords: enumeration, labeled graph, connected graph, 2-connected graph, generating function, block-stable class, series-parallel graph. 
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V. A. Voblyi. The second Riddel relation and its consequences. Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 1, pp. 20-32. http://geodesic.mathdoc.fr/item/DA_2019_26_1_a1/