Are all regular graphs isomorphic?

I have been trying to solve a question and this has arisen as a subproblem. I have a feeling the above statement is true, however haven't been able to come up with a proof (or a counterexample)...

Thanks.

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Originally Posted by DaRush19

I have been trying to solve a question and this has arisen as a subproblem. I have a feeling the above statement is true, however haven't been able to come up with a proof (or a counterexample)...

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Here are two non-isomorphic 2regular graphs of order six.

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Originally Posted by Plato

Here are two non-isomorphic 2regular graphs of order six.

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What about all connected regular graphs?

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Originally Posted by DaRush19

What about all connected regular graphs?

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