added dual graph

doc/planar.xml

@@ -427,3 +427,34 @@ fail
   </Description>
 </ManSection>
 <#/GAPDoc>
+
+<#GAPDoc Label="DualPlanarGraph">
+<ManSection>
+  <Attr Name="DualPlanarGraph" Arg="digraph"/>
+  <Returns>A digraph or <K>fail</K>.</Returns>
+  <Description>
+    If <A>digraph</A> is a planar digraph, then <E>DualPlanarGraph</E> returns the the dual graph of <A>digraph</A>.
+    If <A>digraph</A> is not planar, then fail is returned.<P/>
+
+    The dual graph of a planar digraph <A>digraph</A> has a vertex for each face of <A>digraph</A> and an edge for 
+    each pair of faces that are separated by an edge from each other.
+    Vertex <A>i</A> of the dual graph corresponds to the facial walk at the <A>i</A>-th position calling 
+    <E>FacialWalks</E> of <A>digraph</A> with the rotation system returned by <E>PlanarEmbedding</E>.
+
+<Example><![CDATA[
+gap> D := CompleteDigraph(4);;
+gap> dualD := DualPlanarGraph(D);
+<immutable digraph with 4 vertices, 12 edges>
+gap> IsIsomorphicDigraph(D, dualD);
+true
+gap> cube := Digraph([[2, 4, 5], [1, 3, 6], [2, 4, 7], [1, 3, 8], 
+>                     [1, 6, 8], [2, 5, 7], [3, 6, 8], [4, 5, 7]]);
+<immutable digraph with 8 vertices, 24 edges>
+gap> oct := DualPlanarGraph(cube);;
+gap> IsIsomorphicDigraph(oct, CompleteMultipartiteDigraph([2, 2, 2]));
+true
+]]></Example>
+  </Description>
+</ManSection>
+
+<#/GAPDoc>

doc/z-chap4.xml

@@ -106,6 +106,7 @@
     <#Include Label="PlanarEmbedding">
     <#Include Label="OuterPlanarEmbedding">
     <#Include Label="SubdigraphHomeomorphicToK">
+    <#Include Label="DualPlanarGraph">
   </Section>
 
   <Section><Heading>Hashing</Heading>

gap/planar.gd

@@ -25,6 +25,7 @@ DeclareAttribute("KuratowskiOuterPlanarSubdigraph", IsDigraph);
 DeclareAttribute("SubdigraphHomeomorphicToK23", IsDigraph);
 DeclareAttribute("SubdigraphHomeomorphicToK4", IsDigraph);
 DeclareAttribute("SubdigraphHomeomorphicToK33", IsDigraph);
+DeclareAttribute("DualPlanarGraph", IsDigraph);
 
 # Properties . . .
 

gap/planar.gi

@@ -73,6 +73,47 @@ SUBGRAPH_HOMEOMORPHIC_TO_K4);
 InstallMethod(SubdigraphHomeomorphicToK33, "for a digraph", [IsDigraph],
 SUBGRAPH_HOMEOMORPHIC_TO_K33);
 
+InstallMethod(DualPlanarGraph, "for a digraph", [IsDigraph],
+function(D)
+  local digraph, rotationSystem, facialWalks, dualEdges,
+        cycle1, cycle2, commonNodes, i;
+
+    if not IsPlanarDigraph(D) then
+        return fail;
+    fi;
+
+    digraph := DigraphSymmetricClosure(DigraphRemoveLoops(
+        DigraphRemoveAllMultipleEdges(DigraphMutableCopyIfMutable(D))));
+    rotationSystem := PlanarEmbedding(digraph);
+    facialWalks := FacialWalks(digraph, rotationSystem);
+
+    dualEdges := [];
+    for cycle1 in [1 .. Length(facialWalks) - 1] do
+        for cycle2 in [cycle1 .. Length(facialWalks)] do
+            if cycle1 = cycle2 then
+                if not IsDuplicateFree(facialWalks[cycle1]) then
+                    Add(dualEdges, [cycle1, cycle1]);
+                fi;
+            else
+                commonNodes := Intersection(facialWalks[cycle1],
+                                            facialWalks[cycle2]);
+                if Length(commonNodes) = Length(facialWalks[cycle1]) then
+                    for i in [1 .. Length(commonNodes)] do
+                        Add(dualEdges, [cycle1, cycle2]);
+                        Add(dualEdges, [cycle2, cycle1]);
+                    od;
+                else
+                    for i in [1 .. Length(commonNodes) - 1] do
+                        Add(dualEdges, [cycle1, cycle2]);
+                        Add(dualEdges, [cycle2, cycle1]);
+                    od;
+                fi;
+            fi;
+        od;
+    od;
+    return DigraphByEdges(dualEdges);
+end);
+
 ########################################################################
 # 2. Properties
 ########################################################################

tst/standard/attr.tst

@@ -1074,11 +1074,11 @@ gap> DigraphAllUndirectedSimpleCircuits(g);
 # FacialCycles
 gap> g := Digraph([]);;
 gap> rotationSy := [];;
-gap> FacialWalks(g,rotationSy);
+gap> FacialWalks(g, rotationSy);
 [  ]
-gap> g := Digraph([[2],[1,3],[2,4],[3]]);;;
-gap> rotationSy := [[2],[1,3],[2,4],[3]];;
-gap> FacialWalks(g,rotationSy);
+gap> g := Digraph([[2], [1, 3], [2, 4], [3]]);;;
+gap> rotationSy := [[2], [1, 3], [2, 4], [3]];;
+gap> FacialWalks(g, rotationSy);
 [ [ 1, 2, 3, 4, 3, 2 ] ]
 gap> g := CycleDigraph(4);;
 gap> planar := PlanarEmbedding(g);
@@ -1095,6 +1095,13 @@ gap> rotationSystem := PlanarEmbedding(g);
 gap> FacialWalks(g, rotationSystem);
 [ [ 1, 3, 6 ], [ 1, 4, 5 ], [ 1, 5, 3 ], [ 1, 6, 4 ], [ 2, 3, 5 ], 
   [ 2, 4, 6 ], [ 2, 5, 4 ], [ 2, 6, 3 ] ]
+gap> g := Digraph([[2, 3, 4], [1, 3, 5], [1, 2, 4], [1, 3, 5], [2, 4, 6], [5, 7, 9], [6, 8, 10], [7, 9, 10], [6, 8, 10], [7, 8, 9]]);;
+gap> rotationSy := PlanarEmbedding(g);
+[ [ 2, 4, 3 ], [ 3, 5, 1 ], [ 1, 4, 2 ], [ 1, 5, 3 ], [ 2, 4, 6 ], 
+  [ 5, 7, 9 ], [ 8, 10, 6 ], [ 9, 10, 7 ], [ 6, 10, 8 ], [ 7, 8, 9 ] ]
+gap> FacialWalks(g, rotationSy);
+[ [ 1, 2, 3 ], [ 1, 3, 4 ], [ 1, 4, 5, 6, 7, 8, 9, 6, 5, 2 ], [ 2, 5, 4, 3 ], 
+  [ 6, 9, 10, 7 ], [ 7, 10, 8 ], [ 8, 10, 9 ] ]
 
 #  Issue #676
 gap> D := Digraph([[], [3], []]);;

tst/standard/planar.tst

@@ -230,6 +230,26 @@ gap> D := CompleteDigraph(3);
 gap> KuratowskiOuterPlanarSubdigraph(D);
 fail
 
+# DualPlanarGraph
+gap> DualPlanarGraph(CompleteDigraph(5));
+fail
+gap> D := CycleDigraph(4);
+<immutable cycle digraph with 4 vertices>
+gap> DualPlanarGraph(D);
+<immutable multidigraph with 2 vertices, 8 edges>
+gap> D := ChainDigraph(4);
+<immutable chain digraph with 4 vertices>
+gap> DualPlanarGraph(D);
+<immutable empty digraph with 0 vertices>
+gap> D := Digraph([[2, 3, 4], [1, 3, 5], [1, 2, 4], [1, 3, 5], [2, 4, 6], [5, 7, 9], [6, 8, 10], [7, 9, 10], [6, 8, 10], [7, 8, 9]]);;
+gap> dualD := DualPlanarGraph(D);
+<immutable multidigraph with 7 vertices, 29 edges>
+gap> DigraphHasLoops(dualD);
+true
+gap> D := CompleteDigraph(3);;
+gap> DualPlanarGraph(D);
+<immutable multidigraph with 2 vertices, 6 edges>
+
 # Kernel function boyers_planarity_check, errors
 gap> IS_PLANAR(2);
 Error, Digraphs: boyers_planarity_check (C): the 1st argument must be a digrap\