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This resolves the following bug:

gap> G:=CompleteBipartiteDigraph(1,5);
<immutable complete bipartite digraph with bicomponent sizes 1 and 5>
gap> DigraphBicomponents(G);
[ [ 1 ], [ 2, 3, 4, 5, 6 ] ]
gap> AutomorphismGroup(G);
Group([ (1,2,3,4,5), (1,2) ])

Simply put, our code was assuming that for DirectProduct(SymmetricGroup([1]), SymmetricGroup([2..6])), GAP would return SymmetricGroup([2..6]). But in fact, GAP returns (the isomorphic, but not identical) SymmetricGroup([1..5]).

This bug is what was behind the wrong result reported by @bojankuzma000 in #850.

@wilfwilson wilfwilson added the bugfix A label for PRs that fix a bug label Sep 26, 2025
@wilfwilson wilfwilson linked an issue Sep 26, 2025 that may be closed by this pull request
@wilfwilson wilfwilson changed the title Fix AutomorphismGroup for CompleteBipartiteDigraph(1, n) Fix AutomorphismGroup for CompleteBipartiteDigraph(1,n) Sep 26, 2025
Simply put, our code was assuming that for
`DirectProduct(SymmetricGroup([1]), SymmetricGroup([2..6]))`, GAP would
return `SymmetricGroup([2..6])`. But in fact, GAP returns (the
isomorphic, but not identical) `SymmetricGroup([1..5])`.

Resolves digraphs#850
@wilfwilson wilfwilson merged commit df9fe88 into digraphs:stable-1.13 Sep 26, 2025
32 checks passed
@wilfwilson wilfwilson deleted the fix-issue-850 branch September 26, 2025 12:13
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Digraph(Graph(G)) may not return a graph isomorphic to G

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