For each of the following, give a graph that is a tree contains at most 15 nodes, has at most one arc into any node, and at most two arcs out of any node.

(a) A graph where depth-rst search expands fewer nodes than breadth-rst search.

(b) A graph where breadth-rst search expands fewer nodes than depth-rst search.

You must draw the graph and show the order of the neighbors (this is needed for the depth-rst search). Either give the arc costs and heuristic function or state explicitly that you are drawing the graph to scale and are using Euclidean distance for the arc costs and the heuristic function. Explain why the graph you give is a solution to the problem.