Add HaarGraph

doc/examples.xml

@@ -389,3 +389,50 @@ gap> KnightsGraph(IsMutable, 3, 9);
   </Description>
 </ManSection>
 <#/GAPDoc>
+
+<#GAPDoc Label="HaarGraph">
+<ManSection>
+  <Oper Name="HaarGraph" Arg="[filt, ]n"/>
+  <Returns>A digraph.</Returns>
+  <Description>
+    If <A>n</A> is a positive integer then this operation returns
+    the <E>Haar graph</E> <M>H(<A>n</A>)</M>. <P/>
+
+    From
+    <URL>https://mathworld.wolfram.com/HaarGraph.html</URL>:
+    <P/>
+
+    <Q>A Haar graph H(<A>n</A>) is a bipartite regular vertex-transitive graph
+    indexed by a positive integer and obtained by a simple binary encoding of
+    cyclically adjacent vertices. Haar graphs may be connected or
+    disconnected.</Q><P/>
+
+    The number of vertices in the Haar graph <M>H(<A>n</A>)</M> is
+    equal to twice <M>m</M>, where <M>m</M> is the number of digits
+    required to represent <A>n</A> in binary.
+    These vertices are arranged into bicomponents
+    <C>[1..m]</C> and <C>[m+1..2*m]</C>.
+    Vertices <M>i</M> and <M>j</M> in different bicomponents are
+    adjacent by a symmetric pair of edges if and only if
+    the binary representation of <A>n</A> has a 1 in position
+    (<M>j-i</M> modulo <M>m</M>) + 1 from the left. <P/>
+
+    If the optional first argument <A>filt</A> is present, then this should
+    specify the category or representation the digraph being created will
+    belong to. For example, if <A>filt</A> is <Ref Filt="IsMutableDigraph"/>,
+    then the digraph being created will be mutable, if <A>filt</A> is <Ref
+    Filt="IsImmutableDigraph"/>, then the digraph will be immutable.
+    If the optional first argument <A>filt</A> is not present, then <Ref
+      Filt="IsImmutableDigraph"/> is used by default.<P/>
+
+<Example><![CDATA[
+gap> HaarGraph(3);
+<immutable bipartite vertex-transitive symmetric digraph with bicompon\
+ent sizes 2 and 2>
+gap> D := HaarGraph(16);
+<immutable bipartite vertex-transitive symmetric digraph with bicompon\
+ent sizes 5 and 5>
+]]></Example>
+  </Description>
+</ManSection>
+<#/GAPDoc>

doc/z-chap2.xml

@@ -87,6 +87,7 @@
     <#Include Label="JohnsonDigraph">
     <#Include Label="PetersenGraph">
     <#Include Label="GeneralisedPetersenGraph">
+    <#Include Label="HaarGraph">
     <#Include Label="KnightsGraph">
     <#Include Label="StarDigraph">
   </Section>

gap/examples.gd

@@ -56,3 +56,7 @@ DeclareOperation("StarDigraph", [IsFunction, IsPosInt]);
 DeclareConstructor("KnightsGraphCons", [IsDigraph, IsPosInt, IsPosInt]);
 DeclareOperation("KnightsGraph", [IsPosInt, IsPosInt]);
 DeclareOperation("KnightsGraph", [IsFunction, IsPosInt, IsPosInt]);
+
+DeclareConstructor("HaarGraphCons", [IsDigraph, IsPosInt]);
+DeclareOperation("HaarGraph", [IsPosInt]);
+DeclareOperation("HaarGraph", [IsFunction, IsPosInt]);

gap/examples.gi

@@ -446,3 +446,44 @@ KnightsGraphCons);
 
 InstallMethod(KnightsGraph, "for two positive integers", [IsPosInt, IsPosInt],
 {m, n} -> KnightsGraphCons(IsImmutableDigraph, m, n));
+
+InstallMethod(HaarGraphCons,
+"for IsMutableDigraph and a positive integer",
+[IsMutableDigraph, IsPosInt],
+function(filt, n)
+  local m, binaryList, D, i, j;
+  m := Log(n, 2) + 1;
+  binaryList := DIGRAPHS_BlistNumber(n + 1, m);
+  D := EmptyDigraph(IsMutableDigraph, 2 * m);
+
+  for i in [1 .. m] do
+    for j in [1 .. m] do
+      if binaryList[((j - i) mod m) + 1] then
+          DigraphAddEdge(D, [i, m + j]);
+      fi;
+    od;
+  od;
+
+  return DigraphSymmetricClosure(D);
+end);
+
+InstallMethod(HaarGraphCons,
+"for IsImmutableDigraph and a positive integer",
+[IsImmutableDigraph, IsPosInt],
+function(filt, n)
+  local D;
+  D := MakeImmutable(HaarGraphCons(IsMutableDigraph, n));
+  SetIsMultiDigraph(D, false);
+  SetIsSymmetricDigraph(D, true);
+  SetIsRegularDigraph(D, true);
+  SetIsVertexTransitive(D, true);
+  SetIsBipartiteDigraph(D, true);
+  return D;
+end);
+
+InstallMethod(HaarGraph, "for a function and a positive integer",
+[IsFunction, IsPosInt],
+HaarGraphCons);
+
+InstallMethod(HaarGraph, "for a positive integer", [IsPosInt],
+{n} -> HaarGraphCons(IsImmutableDigraph, n));

gap/utils.gd

@@ -23,3 +23,5 @@ DeclareGlobalFunction("DigraphsTestExtreme");
 DeclareGlobalFunction("DigraphsTestInstall");
 DeclareGlobalFunction("DigraphsTestStandard");
 DeclareGlobalFunction("DigraphsTestManualExamples");
+
+DeclareGlobalFunction("DIGRAPHS_BlistNumber");

gap/utils.gi

@@ -555,3 +555,21 @@ DIGRAPHS_CheckManualConsistency := function()
   DIGRAPHS_CheckDocCoverage(doc);
   return DIGRAPHS_CheckManSectionTypes(doc, true);
 end;
+
+InstallGlobalFunction(DIGRAPHS_BlistNumber,
+function(nr, n)
+  local x, q, i;
+
+  x := BlistList([1 .. n], []);
+  nr := nr - 1;   # to be in [0 .. 2 ^ n - 1]
+  for i in [n, n - 1 .. 1] do
+    q := nr mod 2;
+    if q = 0 then
+      x[i] := false;
+    else
+      x[i] := true;
+    fi;
+    nr := (nr - q) / 2;
+  od;
+  return x;
+end);

tst/standard/examples.tst

@@ -252,6 +252,28 @@ false
 gap> KnightsGraph(IsMutable, 3, 9);
 <mutable digraph with 27 vertices, 88 edges>
 
+# DIGRAPHS_HaarGraph
+gap> HaarGraph(1);
+<immutable bipartite vertex-transitive symmetric digraph with bicomponent size\
+s 1 and 1>
+gap> OutNeighbours(last);
+[ [ 2 ], [ 1 ] ]
+gap> HaarGraph(2);
+<immutable bipartite vertex-transitive symmetric digraph with bicomponent size\
+s 2 and 2>
+gap> OutNeighbours(last);
+[ [ 3 ], [ 4 ], [ 1 ], [ 2 ] ]
+gap> HaarGraph(3);
+<immutable bipartite vertex-transitive symmetric digraph with bicomponent size\
+s 2 and 2>
+gap> OutNeighbours(last);
+[ [ 3, 4 ], [ 3, 4 ], [ 1, 2 ], [ 1, 2 ] ]
+gap> D := HaarGraph(16);
+<immutable bipartite vertex-transitive symmetric digraph with bicomponent size\
+s 5 and 5>
+gap> IsBipartiteDigraph(D);
+true
+
 #
 gap> DIGRAPHS_StopTest();
 gap> STOP_TEST("Digraphs package: standard/examples.tst", 0);