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Could you help me giving me the number of unicyclic graphs with k vertices and k edges ?

I remind that a unicyclic graph with k vertices and k edges is a tree with k vertices and k-1 edges to wich we add an other one edge wich create a cycle inside this tree (so it isn't a tree anymore).

I don't succeed to find this number in any paper ? I am looking for an explicit formula.

Thank you

Nawak
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  • Labelled unicyclic graphs are counted at this MSE link. – Marko Riedel Dec 16 '14 at 20:49
  • Are you (the OP) interested in counting labelled or unlabelled graphs? Because the notions of graph isomorphism differ, so too will the counts generally differ, with a larger number for labelled than for unlabelled graphs. – hardmath Dec 16 '14 at 23:23

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It's the sequence A001429 in the OEIS.

David Hackenger
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