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There is a graph with nine edges and all vertices of degree 3?

I don't think that this graph exist, but I don't know how to prove it.

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    $\begingroup$ There is such a graph: it looks like a hexagon with all three diagonals. $\endgroup$ – Brian M. Scott Apr 9 '16 at 21:31
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    $\begingroup$ You can also draw it as $K_{3,3}$. $\endgroup$ – Henning Makholm Apr 9 '16 at 21:33
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Well, this graph clearly exists.

enter image description here

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