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You can use the subgraph method, the indices are kept untouched:
sage: G = graphs.PetersenGraph()
sage: G.subgraph([1,2,4,5])
Subgraph of (Petersen graph): Graph on 4 vertices
sage: H = G.subgraph([1,2,4,5])
sage: H.vertices()
[1, 2, 4, 5]
