Hello everyone,

I am pretty new to graph theory in general and was having quite a bit of trouble with this questions. This is just practice for myself after I've read a book describing the basics of graph theory. I was able to make other graphs to satisfy all kinds of conditions, but I am getting totally lost at this bipartite graph. I've tried a lot of different things and am at a loss at this point. I've went several ways and used up multiple sheets of paper trying to solve this and still cannot. Can anyone lend me a helping hand at this? I would very much appreciate it. The graph I am trying to make has to be bi partite, have 12 vertices, each having a degree of over 2, and be a Eulerian circuit and hamilton circuit.

All in all I think graph theory is kind of nifty but I feel like it's a waste of time to keep drawing. Isn't there a sure fire method to making these graphs????

Again, I appreciate any help at all!!!