Implemented checking for vertex/edge transitivity (#165)

doc/attr.xml

@@ -1412,3 +1412,47 @@ gap> OutNeighbours(D);
   </Description>
 </ManSection>
 <#/GAPDoc>
+
+<#GAPDoc Label="IsVertexTransitive">
+<ManSection>
+  <Attr Name="IsVertexTransitive" Arg="digraph"/>
+  <Returns><K>true</K> or <K>false</K>.</Returns>
+  <Description>
+    If <A>digraph</A> is a digraph, then <C>IsVertexTransitive</C> returns
+    <K>true</K> if <A>digraph</A> is vertex transitive, and <K>false</K>
+    otherwise. A digraph is <E>vertex transitive</E> if its automorphism group
+    acts transitively on its vertices.
+
+    <Example><![CDATA[
+gap> IsVertexTransitive(Digraph([[1], [2]]));
+true
+gap> IsVertexTransitive(Digraph([[2], [3], []]));
+false
+]]></Example>
+  </Description>
+</ManSection>
+<#/GAPDoc>
+
+<#GAPDoc Label="IsEdgeTransitive">
+<ManSection>
+  <Attr Name="IsEdgeTransitive" Arg="digraph"/>
+  <Returns><K>true</K> or <K>false</K>.</Returns>
+  <Description>
+    If <A>digraph</A> is a digraph without multiple edges, then
+    <C>IsEdgeTransitive</C> returns <K>true</K> if <A>digraph</A>
+    is edge transitive, and <K>false</K> otherwise. A digraph is
+    <E>edge transitive</E> if its automorphism group acts
+    transitively on its edges (via the action <Ref Prop="OnPairs"/>).
+
+    <Example><![CDATA[
+gap> IsEdgeTransitive(Digraph([[1], [2]]));
+true
+gap> IsEdgeTransitive(Digraph([[2], [3], []]));
+false
+gap> IsEdgeTransitive(Digraph([[2], [3, 3, 3], []]));
+Error, Digraphs: IsEdgeTransitive: usage,
+the argument <graph> must not have multiple edges,
+]]></Example>
+  </Description>
+</ManSection>
+<#/GAPDoc>

gap/attr.gd

@@ -77,3 +77,6 @@ DeclareAttribute("HamiltonianPath", IsDigraph);
 DeclareAttribute("AsGraph", IsDigraph, "mutable");
 DeclareAttribute("AsTransformation", IsDigraph);
 DeclareAttribute("DIGRAPHS_ConnectivityData", IsDigraph, "mutable");
+
+DeclareAttribute("IsVertexTransitive", IsDigraph);
+DeclareAttribute("IsEdgeTransitive", IsDigraph);

gap/attr.gi

@@ -1537,3 +1537,19 @@ InstallMethod(CharacteristicPolynomial,
 function(gr)
     return CharacteristicPolynomial(AdjacencyMatrix(gr));
 end);
+
+InstallMethod(IsVertexTransitive, "for a digraph",
+[IsDigraph],
+gr -> IsTransitive(AutomorphismGroup(gr), DigraphVertices(gr)));
+
+InstallMethod(IsEdgeTransitive, "for a digraph",
+[IsDigraph],
+function(digraph)
+  if IsMultiDigraph(digraph) then
+    ErrorNoReturn("Digraphs: IsEdgeTransitive: usage,\n",
+                  "the argument <digraph> must not have multiple edges,");
+  fi;
+  return IsTransitive(AutomorphismGroup(digraph),
+                      DigraphEdges(digraph),
+                      OnPairs);
+end);

tst/standard/attr.tst

@@ -1721,6 +1721,29 @@ gap> gr := CompleteDigraph(5);
 gap> CharacteristicPolynomial(gr);
 x_1^5-10*x_1^3-20*x_1^2-15*x_1-4
 
+# IsVertexTransitive
+gap> IsVertexTransitive(Digraph([]));
+true
+gap> IsVertexTransitive(Digraph([[1], [2]]));
+true
+gap> IsVertexTransitive(Digraph([[2], [3], []]));
+false
+gap> IsVertexTransitive(CompleteDigraph(20));
+true
+
+# IsEdgeTransitive
+gap> IsEdgeTransitive(Digraph([]));
+true
+gap> IsEdgeTransitive(Digraph([[1], [2]]));
+true
+gap> IsEdgeTransitive(Digraph([[2], [3], []]));
+false
+gap> IsEdgeTransitive(CompleteDigraph(20));
+true
+gap> IsEdgeTransitive(Digraph([[2], [3, 3, 3], []]));
+Error, Digraphs: IsEdgeTransitive: usage,
+the argument <digraph> must not have multiple edges,
+
 #  DIGRAPHS_UnbindVariables
 gap> Unbind(adj);
 gap> Unbind(adj1);