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Perform a depth-first search on the given graph, choosing αbetically first vertices when there is a choice. Classify each edge as a tree or back edge and provide the discovery and finishing time of each vertex.

a) Tree/Back Edge, Discovery/Finishing Time
b) Classification, Time Stamp
c) αbetical Order, Edge Type
d) Graph Analysis, Vertex Time

User An Hoa
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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.

User Nikitah
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