# Graph Theory Hamiltonian Question

• Dec 15th 2009, 07:04 PM
gummy_ratz
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!
• Dec 15th 2009, 08:41 PM
gummy_ratz
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