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Fix AutomorphismGroup for CompleteBipartiteDigraph(1,n) #852

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Sep 26, 2025
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Fix AutomorphismGroup for CompleteBipartiteDigraph(1,n) #852

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12 changes: 10 additions & 2 deletions gap/examples.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -68,14 +68,22 @@ InstallMethod(CompleteBipartiteDigraphCons,
[IsImmutableDigraph, IsPosInt, IsPosInt],
function(_, m, n)
local D, aut;

if Maximum(m, n) = 1 then
return CompleteDigraph(IsImmutableDigraph, 2);
fi;

D := MakeImmutable(CompleteBipartiteDigraph(IsMutableDigraph, m, n));
SetIsSymmetricDigraph(D, true);
SetDigraphNrEdges(D, 2 * m * n);
SetIsCompleteBipartiteDigraph(D, true);
if m = n then
aut := WreathProduct(SymmetricGroup(m), Group((1, 2)));
aut := WreathProduct(SymmetricGroup([1 .. m]), Group((1, m + 1)));
elif m = 1 then
aut := SymmetricGroup([2 .. n + 1]);
else
aut := DirectProduct(SymmetricGroup(m), SymmetricGroup(n));
aut := DirectProduct(SymmetricGroup([1 .. m]),
SymmetricGroup([m + 1 .. m + n]));
fi;
SetAutomorphismGroup(D, aut);
SetIsPlanarDigraph(D, m <= 2 or n <= 2);
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27 changes: 27 additions & 0 deletions tst/testinstall.tst
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Expand Up @@ -509,6 +509,33 @@ rec( comps := [ ], id := [ ] )
gap> IsConnectedDigraph(D);
true

# Issue #850: Problems with AutomorphismGroup for CompleteBipartiteDigraph
gap> D := CompleteBipartiteDigraph(1, 5);
<immutable complete bipartite digraph with bicomponent sizes 1 and 5>
gap> AutomorphismGroup(D) = SymmetricGroup([2 .. 6]);
true
gap> not DIGRAPHS_IsGrapeLoaded() or
> (DIGRAPHS_IsGrapeLoaded() and
> IsomorphismDigraphs(Digraph(Graph(D)), D) <> fail);
true
gap> not DIGRAPHS_IsGrapeLoaded() or
> (DIGRAPHS_IsGrapeLoaded() and
> OnDigraphs(D, IsomorphismDigraphs(Digraph(Graph(D)), D)) = D);
true
gap> D := CompleteBipartiteDigraph(5, 1);
<immutable complete bipartite digraph with bicomponent sizes 5 and 1>
gap> AutomorphismGroup(D) = SymmetricGroup([1 .. 5]);
true
gap> D := CompleteBipartiteDigraph(1, 1);
<immutable complete digraph with 2 vertices>
gap> AutomorphismGroup(D) = Group([(1, 2)]);
true
gap> D := CompleteBipartiteDigraph(3, 3);
<immutable complete bipartite digraph with bicomponents of size 3>
gap> AutomorphismGroup(D)
> = Group([(1, 2, 3), (1, 2), (4, 5, 6), (4, 5), (1, 4)(2, 5)(3, 6)]);
true

#
gap> DIGRAPHS_StopTest();
gap> STOP_TEST("Digraphs package: testinstall.tst", 0);
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