I am aware that the number of simple graphs possible with $n$ labelled vertices is $2^{n(n-1)/2}$. Is there any closed formula for the same problem with $n$ unlabelled vertices? In case of unlabelled vertices we have to eliminate graphs that are isomorphic.
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2Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – José Carlos Santos Sep 04 '19 at 03:03
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1This is A000088 There are some formulas given, but I think they are all asymptotics. I don't see an explicit closed-form formula. – saulspatz Sep 04 '19 at 03:18
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1The following MSE link may prove useful. – Marko Riedel Sep 04 '19 at 16:35
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You can find a formula for the counting polynomial using Polya’s Enumeration Theorem as explained in $(3)$ of http://mathworld.wolfram.com/SimpleGraph.html
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