examples: add pancakes

gap/examples.gd

@@ -48,3 +48,5 @@ DeclareOperation("PetersenGraph", [IsFunction]);
 DeclareConstructor("GeneralisedPetersenGraphCons", [IsDigraph, IsInt, IsInt]);
 DeclareOperation("GeneralisedPetersenGraph", [IsInt, IsInt]);
 DeclareOperation("GeneralisedPetersenGraph", [IsFunction, IsInt, IsInt]);
+
+DeclareGlobalFunction("DIGRAPHS_PancakeGraph");

gap/examples.gi

@@ -370,3 +370,49 @@ GeneralisedPetersenGraphCons);
 
 InstallMethod(GeneralisedPetersenGraph, "for integer, integer", [IsInt, IsInt],
 {n, k} -> GeneralisedPetersenGraphCons(IsImmutableDigraph, n, k));
+
+InstallGlobalFunction(DIGRAPHS_PancakeGraph,
+function(n)
+  local PancakeGraphInner;
+
+  PancakeGraphInner := function(list)
+    local D, C, labels, DD, new_labels, extra, w, l, i, v;
+    if Length(list) = 2 then
+      D := Digraph(IsMutableDigraph, [[2], [1]]);
+      SetDigraphVertexLabels(D, [list, Reversed(list)]);
+      return D;
+    fi;
+
+    C := Combinations(list, Length(list) - 1);
+    D := PancakeGraphInner(C[1]);
+    extra := Difference(list, C[1]);
+    labels := DigraphVertexLabels(D);
+    for l in labels do
+      Append(l, extra);
+    od;
+    SetDigraphVertexLabels(D, labels);
+    for i in [2 .. Length(C)] do
+      DD := PancakeGraphInner(C[i]);
+      new_labels := DigraphVertexLabels(DD);
+      extra := Difference(list, C[i]);
+      for l in new_labels do
+        Append(l, extra);
+      od;
+      labels := DigraphVertexLabels(D);
+      Append(labels, new_labels);
+      DigraphDisjointUnion(D, DD);
+      SetDigraphVertexLabels(D, labels);
+    od;
+
+    labels := DigraphVertexLabels(D);
+    for v in DigraphVertices(D) do
+      w := Position(labels, Reversed(labels[v]));
+      if v <> w then
+        DigraphAddEdge(D, v, w);
+      fi;
+    od;
+
+    return D;
+  end;
+  return PancakeGraphInner([1 .. n]);
+end);

tst/standard/examples.tst

@@ -226,6 +226,18 @@ Error, the arguments <n> and <k> must be non-negative integers,
 gap> JohnsonDigraph(IsMutableDigraph, 4, 2);
 <mutable digraph with 6 vertices, 24 edges>
 
+# PancakeGraph
+gap> D := DIGRAPHS_PancakeGraph(3);
+<mutable digraph with 6 vertices, 12 edges>
+gap> ChromaticNumber(D);
+2
+gap> IsVertexTransitive(D);
+true
+gap> DigraphUndirectedGirth(D);
+6
+gap> IsHamiltonianDigraph(D);
+true
+
 #
 gap> DIGRAPHS_StopTest();
 gap> STOP_TEST("Digraphs package: standard/examples.tst", 0);