fix edge placement in HanoiGraph

doc/examples.xml

@@ -1083,7 +1083,7 @@ true]]></Example>
     <E>Hanoi graph</E>. The Hanoi graph's vertices represent the possible states
      of the 'Tower of Hanoi' puzzle on three 'towers', while its edges represent
      possible moves. The Hanoi graph has <C>3^<A>n</A></C> vertices, and
-     <C>Binomial(3, 3) * (3^<A>n</A> - 1) / 2</C> undirected edges.<P/>
+     <C>3 * (3^<A>n</A> - 1) / 2</C> undirected edges.<P/>
 
     The Hanoi graph is Hamiltonian. The graph superficially resembles the
     Sierpinski triangle. The graph is also a 'penny graph' - a graph whose

gap/examples.gi

@@ -1251,22 +1251,29 @@ InstallMethod(HalvedCubeGraph, "for a function and an integer",
 InstallMethod(HanoiGraphCons, "for IsMutableDigraph and an integer",
 [IsMutableDigraph, IsPosInt],
 function(_, n)
-  local D, nrVert, prevNrVert, exp, i;
+  local e, D, nrVert, prevNrVert, anchor1, anchor2, anchor3, i;
   D := Digraph(IsMutableDigraph, []);
   nrVert := 3 ^ n;
   DigraphAddVertices(D, nrVert);
-  DigraphAddEdges(D, [[1, 2], [2, 3], [3, 1]]);
+  e := [[1, 2], [2, 3], [3, 1]];
+  # Anchors correspond to the top, bottom left and bottom right node of the
+  # current graph.
+  anchor1 := 1;
+  anchor2 := 2;
+  anchor3 := 3;
   prevNrVert := 1;
-  exp := 1;
+  # Starting from the triangle graph G := C_3, itteratively triplicate G, and
+  # connect each copy using their anchors.
   for i in [2 .. n] do
     prevNrVert := prevNrVert * 3;
-    DigraphAddEdges(D, Concatenation(DigraphEdges(D) + prevNrVert,
-                                    DigraphEdges(D) + (2 * prevNrVert)));
-    DigraphAddEdge(D, prevNrVert / 2 + (1 / 2), prevNrVert + 1);
-    DigraphAddEdge(D, prevNrVert, 2 * prevNrVert + 1);
-    DigraphAddEdge(D, 2 * prevNrVert, prevNrVert * 3 - exp);
-    exp := exp * 2;
+    Append(e, Concatenation(e + prevNrVert, e + (2 * prevNrVert)));
+    Add(e, [anchor2, anchor1 + prevNrVert]);
+    Add(e, [anchor3, anchor1 + (2 * prevNrVert)]);
+    Add(e, [anchor3 + prevNrVert, anchor2 + (2 * prevNrVert)]);
+    anchor2 := anchor2 + prevNrVert;
+    anchor3 := anchor3 + (2 * prevNrVert);
   od;
+  DigraphAddEdges(D, e);
 
   return DigraphSymmetricClosure(D);
 end);

tst/standard/examples.tst

@@ -575,9 +575,15 @@ gap> D := HanoiGraph(1);
 <immutable Hamiltonian connected symmetric digraph with 3 vertices, 6 edges>
 gap> IsIsomorphicDigraph(D, CycleGraph(3));
 true
-gap> HanoiGraph(4);
+gap> gr := HanoiGraph(4);
 <immutable Hamiltonian connected symmetric digraph with 81 vertices, 240 edges\
 >
+gap> IsPlanarDigraph(gr);
+true
+gap> IsHamiltonianDigraph(gr);
+true
+gap> IsPlanarDigraph(DigraphMutableCopy(gr));
+true
 gap> HanoiGraph(0);
 Error, no method found! For debugging hints type ?Recovery from NoMethodFound
 Error, no 1st choice method found for `HanoiGraph' on 1 arguments