Question: Given an undirected, unweighted, connected graph G , suppose we run a DFS on G starting on some nodes. We find that the DFS tree

Given an undirected, unweighted, connected graph G, suppose we run a DFS on G starting on some nodes. We find that the DFS tree has the property that for any vertex v, the path in the DFS tree from s to v is the shortest (fewest number of edges) path from s to v in G. Then G is a tree.

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