(40 points) Consider the following graph. g a e a. (20 points) Starting at vertex a and resolving ties by the vertex alphabetical order, traverse the graph by depth-first search and construct the corresponding depth-first search tree. Give the order in which the vertices were reached for the first time (pushed onto the traversal stack) and the order in which the vertices became dead ends (popped off the stack). b. (20 points) Starting at vertex a and resolving ties by the vertex alphabetical order, traverse the graph by breadth-first search and construct the corresponding breadth-first search tree. Give the order in which the vertices were reached for the first time (added to the traversal queue)