From d522900f54499322d84995150ed53c967abafd98 Mon Sep 17 00:00:00 2001
From: Borbala Forizs <bori.forizs@gmail.com>
Date: Mon, 19 Oct 2026 10:34:52 +0200
Subject: [PATCH] Add DigraphMaximalQuotients

---
 gap/attr.gd           |  1 +
 gap/attr.gi           | 43 +++++++++++++++++++++++++++
 tst/standard/attr.tst | 68 +++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 112 insertions(+)

diff --git a/gap/attr.gd b/gap/attr.gd
index 09d171f6a..9bc9a8c9c 100644
--- a/gap/attr.gd
+++ b/gap/attr.gd
@@ -74,6 +74,7 @@ DeclareAttribute("ChromaticNumber", IsDigraph);
 DeclareAttribute("DigraphBicomponents", IsDigraph);
 DeclareAttribute("DIGRAPHS_Bipartite", IsDigraph);
 DeclareAttribute("DigraphCore", IsDigraph);
+DeclareAttribute("DigraphMaximalQuotients", IsDigraph);
 
 DeclareAttribute("CharacteristicPolynomial", IsDigraph);
 DeclareAttribute("NrSpanningTrees", IsDigraph);
diff --git a/gap/attr.gi b/gap/attr.gi
index 5025a453f..5101c9cb0 100644
--- a/gap/attr.gi
+++ b/gap/attr.gi
@@ -2409,6 +2409,49 @@ function(D)
   return DigraphVertexLabels(D);
 end);
 
+InstallMethod(DigraphMaximalQuotients, "for a digraph", [IsDigraph],
+function(D)
+  local n, aut, orbs, pairs_to_merge, candidates, c, distinct_canons,
+  max_quotients;
+
+  n := DigraphNrVertices(D);
+  if n < 2 then
+    return [];
+  elif IsEmptyDigraph(D) then
+    return [EmptyDigraph(n - 1)];
+  fi;
+
+  # This is to ensure compatibility with AutomorphismGroup and QuotientDigraph.
+  if IsMultiDigraph(D) then
+    aut := AutomorphismGroup(DigraphRemoveAllMultipleEdges(D));
+  else
+    aut := AutomorphismGroup(D);
+  fi;
+
+  # Creating orbit representatives.
+  orbs := Orbits(aut, Combinations(DigraphVertices(D), 2), OnSets);
+  pairs_to_merge := List(orbs, Representative);
+
+  # Creating list of candidate maximal quotients.
+  candidates := List(pairs_to_merge,
+      pair -> QuotientDigraph(D, Concatenation([pair],
+          List(Difference(DigraphVertices(D), pair), v -> [v]))));
+
+  # Filtering candidate list based on isomorphism.
+  distinct_canons := Set([]);
+  max_quotients := [];
+
+  for c in candidates do
+    AddSet(distinct_canons, BlissCanonicalDigraph(c));
+    
+    if Length(distinct_canons) > Length(max_quotients) then
+      Add(max_quotients, c);
+    fi;
+  od;
+
+  return max_quotients;
+end);
+
 InstallMethod(CharacteristicPolynomial, "for a digraph", [IsDigraph],
 D -> CharacteristicPolynomial(AdjacencyMatrix(D)));
 
diff --git a/tst/standard/attr.tst b/tst/standard/attr.tst
index d1108e071..f1b44247b 100644
--- a/tst/standard/attr.tst
+++ b/tst/standard/attr.tst
@@ -2522,6 +2522,74 @@ gap> D := Digraph([[2], [1, 3], []]);;
 gap> DigraphCore(D);
 [ 1, 2 ]
 
+# DigraphMaximalQuotients
+gap> DigraphMaximalQuotients(EmptyDigraph(0));
+[  ]
+gap> DigraphMaximalQuotients(EmptyDigraph(1));
+[  ]
+gap> DigraphMaximalQuotients(EmptyDigraph(5));
+[ <immutable empty digraph with 4 vertices> ]
+gap> DigraphMaximalQuotients(ChainDigraph(2)) = [Digraph([[1]])];
+true
+gap> DigraphMaximalQuotients(CompleteDigraph(2)) = [Digraph([[1]])];
+true
+gap> mq := DigraphMaximalQuotients(CompleteDigraph(5));;
+gap> Length(mq) = 1;
+true
+gap> DigraphNrVertices(mq[1]) = 4;
+true
+gap> DigraphNrEdges(mq[1]) = 13;
+true
+gap> DigraphNrLoops(mq[1]) = 1;
+true
+gap> mq := DigraphMaximalQuotients(ChainDigraph(3));;
+gap> Length(mq) = 3;
+true
+gap> ForAll([Digraph([[1, 2], []]), Digraph([[2], [2]]), Digraph([[2], [1]])],
+>       d -> ForAny(mq, q -> IsIsomorphicDigraph(d, q)));
+true
+gap> mq := DigraphMaximalQuotients(Digraph([[2], [], []]));;
+gap> Length(mq) = 2;
+true
+gap> ForAll([Digraph([[1], []]), Digraph([[2], []])],
+>       d -> ForAny(mq, q -> IsIsomorphicDigraph(d, q)));
+true
+gap> mq := DigraphMaximalQuotients(CycleDigraph(4));;
+gap> Length(mq) = 2;
+true
+gap> ForAll([Digraph([[2], [2, 3], [1]]), Digraph([[2], [1, 3], [2]])], 
+>       d -> ForAny(mq, q -> IsIsomorphicDigraph(d, q)));
+true
+gap> D := Digraph([[2, 2], [3], [3]]);
+<immutable multidigraph with 3 vertices, 4 edges>
+gap> mq := DigraphMaximalQuotients(D);;
+gap> Length(mq) = 3;
+true
+gap> ForAny(mq, q -> IsMultiDigraph(q));
+false
+gap> ForAll([Digraph([[1, 2], [2]]), Digraph([[2], [2]]), Digraph([[2], [1, 2]])],
+>       d -> ForAny(mq, q -> IsIsomorphicDigraph(d, q)));
+true
+gap> mq := DigraphMaximalQuotients(BinaryTree(3));;
+gap> Length(mq) = 7;
+true
+gap> ForAll(Combinations(mq, 2), p -> not IsIsomorphicDigraph(p[1], p[2]));
+true
+gap> ForAll(mq, q -> DigraphNrVertices(q) = 6);
+true
+gap> D := RandomDigraph(6, 0.6);;
+gap> mq := DigraphMaximalQuotients(D);;
+gap> ForAll(mq, q -> DigraphNrVertices(q) = 5);
+true
+gap> ForAll(Combinations(mq, 2), p -> not IsIsomorphicDigraph(p[1], p[2]));
+true
+gap> mq2 := DigraphMaximalQuotients(OnDigraphs(D, (1, 2, 3, 4, 5, 6)));;
+gap> Length(mq) = Length(mq2);
+true
+gap> ForAll(mq, q -> ForAny(mq2, r -> IsIsomorphicDigraph(q, r)))
+>     and ForAll(mq2, q -> ForAny(mq, r -> IsIsomorphicDigraph(q, r)));
+true
+
 # MaximalAntiSymmetricSubdigraph
 gap> MaximalAntiSymmetricSubdigraph(Digraph([[2, 2], [1]]));
 <immutable antisymmetric digraph with 2 vertices, 1 edge>