sage: g = graphs.CycleGraph(4)
sage: list(g.depth_first_search(0))
[0, 3, 2, 1]
sage: g.relabel([0,3,2,1])
sage: list(g.depth_first_search(0))
[0, 1, 2, 3]

I was expecting to get [0,3,2,1]  again after relabeling.

Dave

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