I want to create graphs where each vertex has three edges, and is connected by these three edges to three distinct vertices.(adsbygoogle = window.adsbygoogle || []).push({});

I'd like to know the number of vertices for which this is possible. By playing around a bit, I've found that it's possible for graphs with 4, 8, and 12 vertices. If v is the number of vertices, it's easy to see that a necessary (but not sufficient) condition is that [tex]3v/2 \equiv 0 (mod 3) [/tex].

The attached image shows exactly what I'm looking for. The graphs for the tetrahedron, cube, and dodecahedron all satisfy my criteria, while the others do not.

Thanks in advance!

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# Basic Graph Theory Question

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