Consider the following state space for systematically solving the problem: State: A set of vertices, no two of which are connected by an edge. Successor to state S : Add some vertex V to S such that (a) V is alphabetically later than the vertices in S (to guarantee systematic search); (b) V is not connected to any vertex in S. 1 Start state: The empty set. Goal state: A state that attains the target value. Show the part of the state space that would be generated if you use depth-first search in this state space to find the solution to graph 2 with T=21. You should show this as a tree. I recommend drawing trees for assignments left-to-right typewriter format like this: If you want to use graphics software to make a nice looking tree, that's even better, though more work for you. If you want to draw it out and photograph it, that's OK, though less preferred