Final Answer:
a) Tree/Back Edge, Discovery/Finishing Time
Step-by-step explanation:
In a depth-first search (DFS) of a graph, vertices are visited and explored in a recursive manner. The classification of edges involves distinguishing between tree edges, which lead to unvisited vertices, and back edges, which connect to already visited vertices. Additionally, each vertex is assigned a discovery time when it is first encountered and a finishing time when its exploration is complete.
In the context of DFS, a tree edge is formed when moving from the current vertex to a previously unvisited vertex, forming a new branch in the exploration. Back edges, on the other hand, connect to already visited vertices, indicating a cycle in the graph. The discovery time represents when a vertex is first encountered in the DFS process, while the finishing time is assigned when the exploration of that vertex is complete.
Therefore, option a) Tree/Back Edge, Discovery/Finishing Time is the correct choice for the classification of edges and the associated time stamps in a depth-first search.