G = Graph('A_', immutable=True)
G.set_embedding({0: [1], 1: [0]})
H = G.subgraph([0])
# assert H._embedding == {0: [1]}  # but vertex 1 does not exist in H
H.get_embedding() # LookupError

$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 10.7.beta2, Release Date: 2025-04-29              │
│ Using Python 3.13.3. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ Warning: this is a prerelease version, and it may be unstable.     ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
sage: G = Graph('A_', immutable=True)
....: G.set_embedding({0: [1], 1: [0]})
....: H = G.subgraph([0])
....: # assert H._embedding == {0: [1]}  # but vertex 1 does not exist in H
....: H.get_embedding() # LookupError
....: 
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
File /usr/lib/python3.13/site-packages/sage/graphs/base/static_sparse_backend.pyx:834, in sage.graphs.base.static_sparse_backend.StaticSparseBackend.has_edge (build/cythonized/sage/graphs/base/static_sparse_backend.c:20795)()
    833     u = self._vertex_to_int[u]
--> 834     v = self._vertex_to_int[v]
    835 except KeyError:

KeyError: 1

During handling of the above exception, another exception occurred:

LookupError                               Traceback (most recent call last)
Cell In[1], line 5
      3 H = G.subgraph([Integer(0)])
      4 # assert H._embedding == {0: [1]}  # but vertex 1 does not exist in H
----> 5 H.get_embedding() # LookupError

File /usr/lib/python3.13/site-packages/sage/graphs/generic_graph.py:3339, in GenericGraph.get_embedding(self)
   3337 while i < len(embedding[u]):
   3338     v = embedding[u][i]
-> 3339     if not (self.has_edge(u, v) or self.has_edge(v, u)):
   3340         del embedding[u][i]
   3341     else:

File /usr/lib/python3.13/site-packages/sage/graphs/generic_graph.py:13264, in GenericGraph.has_edge(self, u, v, label)
  13262             u, v = u
  13263             label = None
> 13264 return self._backend.has_edge(u, v, label)

File /usr/lib/python3.13/site-packages/sage/graphs/base/static_sparse_backend.pyx:836, in sage.graphs.base.static_sparse_backend.StaticSparseBackend.has_edge (build/cythonized/sage/graphs/base/static_sparse_backend.c:20841)()
    834     v = self._vertex_to_int[v]
    835 except KeyError:
--> 836     raise LookupError("one of the two vertices does not belong to the graph")
    837 
    838 return self._has_labeled_edge_unsafe(u, v, l)

LookupError: one of the two vertices does not belong to the graph