Question

Perform a depth-first search on the following graph; whenever there is a choice of vertices, pick the one that is αbetically first. Classify each edge as a tree or back edge and give the discovery and finishing time of each vertex (assuming we start at 1, that is, the first vertex is discovered at time 1).

Answer 1

Performing a depth-first search on a graph involves starting at a specific vertex and exploring as far as possible along each branch before backtracking. The graph can be traversed by choosing the alphabetical order for vertices. The discovery and finishing time of each vertex can be recorded during the traversal.

Step-by-step explanation:

A depth-first search is a graph traversal algorithm that starts at a specific vertex and explores as far as possible along each branch before backtracking. To perform a depth-first search on the given graph, we start at vertex 1 (discovered at time 1) and choose alphabetical order for vertices. We continue visiting unvisited neighbors until we reach a dead end, then backtrack. We classify edges as tree edges if they lead to unvisited vertices and back edges if they lead to visited vertices. The discovery and finishing time of each vertex can be recorded as we traverse the graph.