Thread: Graph Theory Hamiltonian Question

This should be a really easy question I think.... my brain is just not working properly, and I'm circling around. I'm looking to draw a 10 vertice, 2-connected graph G, with max valency four, where G^2 is hamiltonian. .... And it seems as though no matter what I use, it should work... because I read that any 2-connected graph's square is hamiltonian, but it's just not working for me. I've been using
0,1,0,1,1,0,0,0,0,0
1,0,1,0,0,0,0,0,0,0
0,1,0,1,1,1,0,0,0,0
1,0,1,0,0,0,0,0,1,0
1,0,1,0,0,0,0,0,0,0
0,0,1,0,0,0,1,0,1,1
0,0,0,0,0,1,0,1,0,0
0,0,0,0,0,0,1,0,1,1
0,0,0,1,0,1,0,1,0,0
0,0,0,0,0,1,0,1,0,0
as my graph, but every time I square it, I get two disjoint graphs... which can't be hamiltonian... please help!

Like, I found a different one that works, I'm pretty sure, but it's just driving me crazy why this one doesn't work.... since I thought it should work in any 2 - connected graph? ee =S