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This is actually the case: the vertices are labelled the same way as in the larger graph, see:
sage: G = graphs.PetersenGraph()
sage: H = graphs.CycleGraph(6)
sage: G.subgraph_search(H)
Subgraph of (Petersen graph): Graph on 6 vertices
sage: G.subgraph_search(H).vertices()
[0, 1, 2, 3, 5, 8]
sage: G.subgraph_search(H).plot()
