combinatoricsdiscrete mathematicsgraph theorygraph-isomorphism
I want to find another graph that has 6 vertices and each has degree $3$ that is not isomorphic to these two graphs below. I know that these two graphs are isomorphic. They will all have the same degree sequence, So I kind of stuck how to find such graph. Any suggestions ?
Hint: A 2-regular graph is a disjoint union of cycles. From there it should be fairly easy to see there are only 2 simple 2-regular graphs on 7 vertices.
One of them has a three cycle. They are both cubic graphs.
Best Answer
Draw two triangles and join them with a 1-factor.