diff --git a/src/sage/graphs/generic_graph.py b/src/sage/graphs/generic_graph.py
index 2ab81f802b2..03850d6fe4b 100644
--- a/src/sage/graphs/generic_graph.py
+++ b/src/sage/graphs/generic_graph.py
@@ -3492,7 +3492,7 @@ def antisymmetric(self):
             True
         """
         if not self._directed:
-            # An undirected graph is antisymmetric only if all it's edges are
+            # An undirected graph is antisymmetric only if all its edges are
             # loops
             return self.size() == len(self.loop_edges())
         if self.has_loops():
@@ -23560,18 +23560,18 @@ def edge_polytope(self, backend=None):
             sage: P.is_combinatorially_isomorphic(polytopes.cross_polytope(3))
             True
 
-        The EP of a graph with edges is isomorphic
-        to the product of it's connected components with edges::
+        The EP of a graph is isomorphic to the subdirect sum of
+        its connected components EPs::
 
-            sage: n = randint(5, 12)
-            sage: G = Graph()
-            sage: while not G.num_edges():
-            ....:     G = graphs.RandomGNP(n, 0.2)
+            sage: n = randint(3, 6)
+            sage: G1 = graphs.RandomGNP(n, 0.2)
+            sage: n = randint(3, 6)
+            sage: G2 = graphs.RandomGNP(n, 0.2)
+            sage: G = G1.disjoint_union(G2)
             sage: P = G.edge_polytope()
-            sage: components = [G.subgraph(c).edge_polytope()
-            ....:               for c in G.connected_components()
-            ....:               if G.subgraph(c).num_edges()]
-            sage: P.is_combinatorially_isomorphic(product(components))
+            sage: P1 = G1.edge_polytope()
+            sage: P2 = G2.edge_polytope()
+            sage: P.is_combinatorially_isomorphic(P1.subdirect_sum(P2))
             True
 
         All trees on `n` vertices have isomorphic EPs::
@@ -23662,18 +23662,18 @@ def symmetric_edge_polytope(self, backend=None):
             sage: P.dim() == n - G.connected_components_number()
             True
 
-        The SEP of a graph with edges is isomorphic
-        to the product of it's connected components with edges::
+        The SEP of a graph is isomorphic to the subdirect sum of
+        its connected components SEP's::
 
-            sage: n = randint(5, 12)
-            sage: G = Graph()
-            sage: while not G.num_edges():
-            ....:     G = graphs.RandomGNP(n, 0.2)
+            sage: n = randint(3, 6)
+            sage: G1 = graphs.RandomGNP(n, 0.2)
+            sage: n = randint(3, 6)
+            sage: G2 = graphs.RandomGNP(n, 0.2)
+            sage: G = G1.disjoint_union(G2)
             sage: P = G.symmetric_edge_polytope()
-            sage: components = [G.subgraph(c).symmetric_edge_polytope()
-            ....:               for c in G.connected_components()
-            ....:               if G.subgraph(c).num_edges()]
-            sage: P.is_combinatorially_isomorphic(product(components))
+            sage: P1 = G1.symmetric_edge_polytope()
+            sage: P2 = G2.symmetric_edge_polytope()
+            sage: P.is_combinatorially_isomorphic(P1.subdirect_sum(P2))
             True
 
         All trees on `n` vertices have isomorphic SEPs::