1. Give a five-node network for which a breadth-first traversal examines the nodes in the same order as a depth-first traversal.
2. Let T be a depth-first search tree of an undirected graph G. Show that for every nontree arc (k, l) in G, either node k is an ancestor of node I in T or node I is an ancestor of node k in T. Show by a counterexample that a breadth-first search tree need not satisfy this property.