Back edges that connect a vertex with its ancestors are part of a depth-first search tree.

Name: Back edges that connect a vertex with its ancestors are part of a depth-first search tree.
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Back edges in a depth-first search (DFS) tree connect a vertex to one of its ancestors, but they are not part of the DFS tree itself; they indicate cycles in the graph and are part of the graph's cycle structure, not the spanning tree structure created by DFS.

Back Edges That Connect a Vertex with Its Ancestors Are