Geodesic
Enumeration of labeled connected graphs with given order and number of edges
Diskretnyj analiz i issledovanie operacij, Tome 23 (2016) no. 2, pp. 5-20

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We deduce a new formula for the number of labeled connected graphs with a given order and number of edges in terms of the block generating function. Applying this formula, we exactly and asymptotically enumerate cacti with given order and cyclomatic number. Tab. 1, bibliogr. 22.
Keywords: enumeration, labeled graph, block, asymptotics.
Mots-clés : cactus 
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V. A. Voblyi. Enumeration of labeled connected graphs with given order and number of edges. Diskretnyj analiz i issledovanie operacij, Tome 23 (2016) no. 2, pp. 5-20. http://geodesic.mathdoc.fr/item/DA_2016_23_2_a0/