USACO - Mother's Milk

I don't know why, but I had a great misunderstanding of the problem statement from this sentence "FJ pours milk from one bucket to another until the second bucket is filled or the first bucket is empty" :-) I thought by second bucket he means bucket B, and by first bucket he means bucket A. But no problem I will pay more attention from now on. So after I understood the problem statement correctly, I thought a little about the "states" in pouring buckets, I felt that I can present each state as a node, and cause each bucket has a capacity from 1 to 20, so we have at most 20*20*20 nodes, we can DFS over all of them and find what can remain at bucket C when bucket A is empty. Now that we have presented nodes, we are facing a graph, graphs do need edges don't they? (Unless we are facing a null graph). So what is an edge in our graph? By edge I mean how can we go from one node to another? Consider first sample input in the problem statement, Suppose this triple as a staring node (0,0,10), what other nodes can we visit directly from this node?

(8,0,2) & (0,9,1) am I right? what happens after that? Just like DFS (or BFS) other nodes that are not visited and can be visited, must be visited :-) (too many 'visited's)