A graph is called simple if there are no loops and there are no multiple edges. Is it possible to compute the number of non-isomorphic, simple, connected graphs with 6 vertices? If the number is known, how we obtain this number? Thank you in advance!
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1$\begingroup$ C'mon, this is not for MO. Just use invariants, one after another: first, the number of edges, then the number of components, the ramification, etc. Children will have fun. $\endgroup$– Wlod AACommented Jul 29, 2022 at 16:29
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1 Answer
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The answer to the question is $112$.
This is available at OEIS:
Number of connected graphs with n nodes
You can enumerate small graphs with Nauty: https://www.mankier.com/1/nauty-geng
Or try the following sagemath code, possibly in a browser:
cou=0
for g0 in graphs(6):
if g0.is_connected(): cou += 1
