From cee4b90aa03808b51b35d76e345a36929a2f63f1 Mon Sep 17 00:00:00 2001
From: dcoudert <david.coudert@inria.fr>
Date: Wed, 8 Jan 2025 13:00:42 +0100
Subject: [PATCH 1/3] faster method __mul__ for graphs

---
 src/sage/graphs/generic_graph.py | 14 +++++++++++---
 1 file changed, 11 insertions(+), 3 deletions(-)

diff --git a/src/sage/graphs/generic_graph.py b/src/sage/graphs/generic_graph.py
index badd28f4fb8..95e8ec74ebd 100644
--- a/src/sage/graphs/generic_graph.py
+++ b/src/sage/graphs/generic_graph.py
@@ -774,9 +774,17 @@ def __mul__(self, n):
                 raise TypeError('multiplication of a graph and a nonpositive integer is not defined')
             if n == 1:
                 return copy(self)
-            return sum([self] * (n - 1), self)
-        else:
-            raise TypeError('multiplication of a graph and something other than an integer is not defined')
+            # Use a logarithmic number of additions to build the result
+            bits = Integer(n).bits()
+            parts = [self]
+            parts.extend(parts[-1] + parts[-1] for _ in range(1, len(bits)))
+            H, _ = parts.pop(), bits.pop()
+            while bits:
+                g, b = parts.pop(), bits.pop()
+                if b:
+                    H += g
+            return H
+        raise TypeError('multiplication of a graph and something other than an integer is not defined')
 
     def __ne__(self, other):
         """

From 6253a319669e644cdba12a0f6178fbe37baa0c07 Mon Sep 17 00:00:00 2001
From: dcoudert <david.coudert@inria.fr>
Date: Wed, 8 Jan 2025 17:55:29 +0100
Subject: [PATCH 2/3] #39300: add doctests

---
 src/sage/graphs/generic_graph.py | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/src/sage/graphs/generic_graph.py b/src/sage/graphs/generic_graph.py
index 95e8ec74ebd..22a350f332b 100644
--- a/src/sage/graphs/generic_graph.py
+++ b/src/sage/graphs/generic_graph.py
@@ -768,6 +768,17 @@ def __mul__(self, n):
             [0, 1, 2, 3, 4, 5, 6, 7, 8]
             sage: H = G * 1; H
             Cycle graph: Graph on 3 vertices
+
+        TESTS::
+
+            sage: Graph(1) * -1
+            Traceback (most recent call last)
+            ...
+            TypeError: multiplication of a graph and a nonpositive integer is not defined
+            sage: Graph(1) * 2.5
+            Traceback (most recent call last)
+            ...
+            TypeError: multiplication of a graph and something other than an integer is not defined
         """
         if isinstance(n, (int, Integer)):
             if n < 1:

From 37729d5470d6de7aaff9314595f6dc449ae44361 Mon Sep 17 00:00:00 2001
From: dcoudert <david.coudert@inria.fr>
Date: Wed, 8 Jan 2025 18:43:40 +0100
Subject: [PATCH 3/3] #39300: correct doctests

---
 src/sage/graphs/generic_graph.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/sage/graphs/generic_graph.py b/src/sage/graphs/generic_graph.py
index 22a350f332b..c2ec7959847 100644
--- a/src/sage/graphs/generic_graph.py
+++ b/src/sage/graphs/generic_graph.py
@@ -772,11 +772,11 @@ def __mul__(self, n):
         TESTS::
 
             sage: Graph(1) * -1
-            Traceback (most recent call last)
+            Traceback (most recent call last):
             ...
             TypeError: multiplication of a graph and a nonpositive integer is not defined
             sage: Graph(1) * 2.5
-            Traceback (most recent call last)
+            Traceback (most recent call last):
             ...
             TypeError: multiplication of a graph and something other than an integer is not defined
         """