# Is there a non-planar, non-hamiltonian and eulerian graph?

I'm trying to find a graph that is non-planar, non-hamiltonian and eulerian but I can't find anyone. Is this possible?

Thanks

Take two copies of $$K_5$$ and identify one of the nodes in one with one of the nodes in the other.
• @emee: What is $v$ and $u$? The condition in Ore's theorem talks about pairs of distinct vertices. The graph I describe has eight vertices of degree 4 and one vertex of degree 8, so how do you get $2\cdot 8$ for even one pair of vertices? – Henning Makholm Dec 12 '18 at 22:44