add method IsDigraphAutomorphism

This operation takes a digraph and a permutation and returns true if the
permutation is an automorphism of the digraph.

doc/isomorph.xml

@@ -811,3 +811,31 @@ gap> OutNeighbours(canon);
   </Description>
 </ManSection>
 <#/GAPDoc>
+
+<#GAPDoc Label="IsDigraphAutomorphism">
+<ManSection>
+  <Oper Name="IsDigraphAutomorphism" Label="for a digraph and permutation"
+    Arg="digraph, x"/>
+  <Returns><K>true</K> or <K>false</K>.</Returns>
+  <Description> 
+    This operation returns true if the permutation <A>x</A> is an automorphism
+    of the digraph <A>digraph</A>. An permutation <C>g</C> on the vertices of a
+    digraph <C>gr</C> is an automorphism if it satisfies: <C>(u, v)</C> is an
+    edge of <C>gr</C> if and only if <C>(g(u), g(v))</C> is an edge of <C>gr</C>
+    for all vertices <C>u</C> and <C>v</C> in digraph. See also <Ref
+      Attr="AutomorphismGroup" Label="for a digraph" />.
+    <Example><![CDATA[
+gap> digraph := Digraph([[1], [1, 2], [1, 3]]);
+<digraph with 3 vertices, 5 edges>
+gap> IsDigraphAutomorphism(digraph, (1, 2, 3));
+false
+gap> IsDigraphAutomorphism(digraph, (2, 3));
+true
+gap> IsDigraphAutomorphism(digraph, (1, 4));
+false
+gap> IsDigraphAutomorphism(digraph, ());
+true
+]]></Example>
+  </Description>
+</ManSection>
+<#/GAPDoc>

gap/isomorph.gd

@@ -43,3 +43,5 @@ DeclareGlobalFunction("DigraphsUseNauty");
 BindGlobal("DIGRAPHS_UsingBliss", true);
 
 DeclareGlobalFunction("DIGRAPHS_ValidateVertexColouring");
+
+DeclareOperation("IsDigraphAutomorphism", [IsDigraph, IsPerm]);

gap/isomorph.gi

@@ -554,3 +554,14 @@ function(n, partition, method)
                 "<partition[i]> is the colour of vertex i; in the second\n",
                 "form, <partition[i]> is the list of vertices with colour i,");
 end);
+
+InstallMethod(IsDigraphAutomorphism,
+"for a digraph and a permutation",
+[IsDigraph, IsPerm],
+function(gr, x)
+  if IsMultiDigraph(gr) then
+    ErrorNoReturn("Digraphs: IsDigraphAutomorphism: usage,\n",
+                  "the first argument <gr> must not have multiple edges,");
+  fi;
+  return OnDigraphs(gr, x) = gr;
+end);

tst/standard/isomorph.tst

@@ -816,6 +816,24 @@ gap> if not nauty then
 >      DigraphsUseBliss();
 >    fi;
 
+# IsDigraphAutomorphism
+gap> gr1 := Digraph([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4], [1]]);
+<digraph with 4 vertices, 13 edges>
+gap> IsDigraphAutomorphism(gr1, (1, 2, 3));
+false
+gap> IsDigraphAutomorphism(gr1, (2, 3));
+true
+gap> IsDigraphAutomorphism(gr1, ());
+true
+gap> gr2 := Digraph([[1], [1, 2], [1, 3], [1, 4], [1, 5], [1, 2, 3, 4, 5, 6]]);
+<digraph with 6 vertices, 15 edges>
+gap> IsDigraphAutomorphism(gr2, (2, 3, 4, 5));
+true
+gap> IsDigraphAutomorphism(gr2, (1, 6));
+false
+gap> IsDigraphAutomorphism(gr2, (6, 7, 8));
+false
+
 #T# DIGRAPHS_UnbindVariables
 gap> Unbind(G);
 gap> Unbind(canon);