Hi all, love this forum. I need a little bit of help with this question.

I have this graph that I need to prove if it is Hamiltonian or not.

http://imageshack.us/photo/my-images/606/unledzw.png/

I have found that it satisfies the necessary condition that if you take U to be a proper set of the vertices, then the sub graph induced by V\U has at most |U| components.

But I don't how to show if it is Hamiltonian or not. So does it satisfy any sufficient condition? Is this

Thanks in advance for any help given.