diff --git a/src/sage/graphs/generic_graph.py b/src/sage/graphs/generic_graph.py
index 969ed45add1..55e9a229763 100644
--- a/src/sage/graphs/generic_graph.py
+++ b/src/sage/graphs/generic_graph.py
@@ -5376,7 +5376,8 @@ def blocks_and_cuts_tree(self):
         to `u`.
 
         The resulting graph is a tree, with the additional characteristic
-        property that the distance between two leaves is even.
+        property that the distance between two leaves is even. When ``self`` is
+        not connected, the resulting graph is a forest.
 
         When ``self`` is biconnected, the tree is reduced to a single node of
         type `B`.
@@ -5408,6 +5409,14 @@ def blocks_and_cuts_tree(self):
             sage: T.vertices()
             [('B', (0, 1, 2, 3, 4, 5, 6, 7, 8, 9))]
 
+        TESTS:
+
+        When ``self`` is not connected, the resulting graph is a forest (:trac:`24163`)::
+
+            sage: T = Graph(2).blocks_and_cuts_tree()
+            sage: T.is_forest()
+            True
+
         REFERENCES:
 
         .. [HarPri] \F. Harary and G. Prins. The block-cutpoint-tree of