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Add DigraphMaximalQuotients #959

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1 change: 1 addition & 0 deletions gap/attr.gd
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Original file line number Diff line number Diff line change
Expand Up @@ -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);
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43 changes: 43 additions & 0 deletions gap/attr.gi
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Expand Up @@ -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)));

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68 changes: 68 additions & 0 deletions tst/standard/attr.tst
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Expand Up @@ -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>
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