sagemathgh-39754: Fix bipartite graph constructor for reduced adjacency matrix with `immutable=True`
    
Related to issue `sagemath#39295`

Previously, when a reduced adjacency matrix was provided and
`immutable=True` was set, the graph construction failed. This fix
ensures that the graph is correctly constructed and behaves as expected.

This issue occurred because the parent class `Graph` constructor was
called with `immutable=True` and then attempted to add vertices and
edges after construction, which is not allowed.

The fix prepares the vertex list and edge list before calling the parent
class constructor with the precomputed vertices and edges.


### 📝 Checklist

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- [x] The title is concise and informative.
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preview.
    
URL: sagemath#39754
Reported by: Ziad Tarek
Reviewer(s): David Coudert, user202729, Ziad Tarek

Author: Release Manager

src/sage/graphs/bipartite_graph.py

@@ -391,6 +391,16 @@ def __init__(self, data=None, partition=None, check=True, hash_labels=None, *arg
             Traceback (most recent call last):
             ...
             LookupError: vertex (7) is not a vertex of the graph
+
+        Check that :issue:`39295` is fixed::
+
+            sage: B = BipartiteGraph(matrix([[1, 1], [1, 1]]), immutable=True)
+            sage: print(B.vertices(), B.edges())
+            [0, 1, 2, 3] [(0, 2, None), (0, 3, None), (1, 2, None), (1, 3, None)]
+            sage: B.add_vertices([4], left=True)
+            Traceback (most recent call last):
+            ...
+            ValueError: graph is immutable; please change a copy instead (use function copy())
         """
         if kwds is None:
             kwds = {'loops': False}
@@ -467,32 +477,31 @@ def __init__(self, data=None, partition=None, check=True, hash_labels=None, *arg
             if kwds.get("multiedges", False) and kwds.get("weighted", False):
                 raise TypeError("weighted multi-edge bipartite graphs from "
                                 "reduced adjacency matrix not supported")
-            Graph.__init__(self, *args, **kwds)
             ncols = data.ncols()
             nrows = data.nrows()
             self.left = set(range(ncols))
             self.right = set(range(ncols, nrows + ncols))
 
-            # ensure that the vertices exist even if there
-            # are no associated edges (trac #10356)
-            self.add_vertices(self.left)
-            self.add_vertices(self.right)
-
-            if kwds.get("multiedges", False):
-                for ii in range(ncols):
-                    for jj in range(nrows):
-                        if data[jj, ii]:
-                            self.add_edges([(ii, jj + ncols)] * data[jj, ii])
-            elif kwds.get("weighted", False):
-                for ii in range(ncols):
-                    for jj in range(nrows):
-                        if data[jj, ii]:
-                            self.add_edge((ii, jj + ncols, data[jj, ii]))
-            else:
-                for ii in range(ncols):
-                    for jj in range(nrows):
-                        if data[jj, ii]:
-                            self.add_edge((ii, jj + ncols))
+            def edges():
+                if kwds.get("multiedges", False):
+                    for ii in range(ncols):
+                        for jj in range(nrows):
+                            for _ in range(data[jj, ii]):
+                                yield (ii, jj + ncols)
+                elif kwds.get("weighted", False):
+                    for ii in range(ncols):
+                        for jj in range(nrows):
+                            if data[jj, ii]:
+                                yield (ii, jj + ncols, data[jj, ii])
+                else:
+                    for ii in range(ncols):
+                        for jj in range(nrows):
+                            if data[jj, ii]:
+                                yield (ii, jj + ncols)
+
+            # ensure that construction works
+            # when immutable=True (issue #39295)
+            Graph.__init__(self, data=[range(nrows + ncols), edges()], format='vertices_and_edges', *args, **kwds)
         else:
             if partition is not None:
                 left, right = set(partition[0]), set(partition[1])