Geodesic
On enumeration of labelled connected graphs by the number of cutpoints
Diskretnaya Matematika, Tome 20 (2008) no. 1, pp. 52-63

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We study the numbers $S_{mn}$ of labelled connected graphs with $n$ vertices among which $m$ are cutpoints. We obtain an explicit expression for the exponential generating function $S_m(z)$ of these numbers and find the asymptotics of the numbers $S_{mn}$ as $n\to\infty$ and $m=o(n)$. 
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     author = {V. A. Voblyi},
     title = {On enumeration of labelled connected graphs by the number of cutpoints},
     journal = {Diskretnaya Matematika},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2008_20_1_a3/}
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V. A. Voblyi. On enumeration of labelled connected graphs by the number of cutpoints. Diskretnaya Matematika, Tome 20 (2008) no. 1, pp. 52-63. http://geodesic.mathdoc.fr/item/DM_2008_20_1_a3/