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Improved title, added enumeration tag, added link to crossposted question
Tony Huynh
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Counting non-isomorphic graphs with prescribed number of edges and vertices

I'd love your help with this question.

Let $n\geq3$ be a fixed integer. How many non-isomorphic graphs with $p$ vertices and $q$ edges are there where $p+q=n$?

Thank you very much.

Crossposted at MSE.