sage: G = Graph([('a', 1), (1, 2), (2, 3)], immutable=True)
sage: type(G._backend)
<class 'sage.graphs.base.static_sparse_backend.StaticSparseBackend'>

sage: G.delete_vertex(1)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
...
ValueError: graph is immutable; please change a copy instead (use function copy())
sage: G.delete_vertex('a')
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
...
ValueError: graph is immutable; please change a copy instead (use function copy())

sage: G.delete_vertex(1)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
...
ValueError: graph is immutable; please change a copy instead (use function copy())
sage: G.delete_vertex('a')
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
...
TypeError: an integer is required