trac #15622: Immutable graphs must not be relabeled

src/sage/graphs/base/static_sparse_backend.pyx

@@ -411,6 +411,22 @@ class StaticSparseBackend(CGraphBackend):
         """
         return v in self._vertex_to_int
 
+    def relabel(self, perm, directed):
+        r"""
+        Relabel the graphs' vertices. No way.
+
+        TEST::
+
+            sage: from sage.graphs.base.static_sparse_backend import StaticSparseCGraph
+            sage: g = StaticSparseCGraph(graphs.PetersenGraph())
+            sage: g.relabel([],True)
+            Traceback (most recent call last):
+            ...
+            ValueError: Thou shalt not remove a vertex from an immutable graph
+
+        """
+        raise ValueError("Thou shalt not relabel an immutable graph")
+
     def get_edge_label(self, object u, object v):
         """
         Returns the edge label for ``(u,v)``.

src/sage/graphs/generic_graph.py

@@ -16386,7 +16386,7 @@ def relabel(self, perm=None, inplace=True, return_map=False, check_input = True,
             sage: G.get_pos()
             {0: (0, 0), 1: (2, 0), 2: (3, 0), 3: (4, 0)}
 
-        Check that #12477 is fixed::
+        Check that :trac:`12477` is fixed::
 
             sage: g = Graph({1:[2,3]})
             sage: rel = {1:'a', 2:'b'}
@@ -16395,17 +16395,26 @@ def relabel(self, perm=None, inplace=True, return_map=False, check_input = True,
             [3, 'a', 'b']
             sage: rel
             {1: 'a', 2: 'b'}
+
+        Immutable graphs cannot be relabeled::
+
+            sage: Graph(graphs.PetersenGraph(), immutable=True).relabel({})
+            Traceback (most recent call last):
+            ...
+            ValueError: Thou shalt not relabel an immutable graph
         """
         from sage.groups.perm_gps.permgroup_element import PermutationGroupElement
 
         if not inplace:
-            from copy import copy
-            G = copy(self)
+            G = self.copy(immutable=False)
             perm2 = G.relabel(perm,
                               return_map= return_map,
                               check_input = check_input,
                               complete_partial_function = complete_partial_function)
 
+            if getattr(self, "_immutable", False):
+                G = self.__class__(G, immutable = True)
+
             if return_map:
                 return G, perm2
             else: