I am interested in undirected, planar, connected graphs where every edge is in a 3-cycle. If there are 4 vertices then, up to isomorphism, there are two such graphs.
How many are there for 5 vertices?
2026-03-27 10:09:39.1774606179
How many different undirected, planar, connected graphs are there where every edge is in a 3-cycle?
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There are really not that many graphs with $5$-vertices up to isomorphism, so this is really just a matter of checking them out. Here are all $34$ of them:
$K_5$ is the only non-planar of the bunch and its easy to get rid the unconnected ones.