Add KnightsGraph

doc/examples.xml

@@ -345,3 +345,47 @@ true
   </Description>
 </ManSection>
 <#/GAPDoc>
+
+<#GAPDoc Label="KnightsGraph">
+<ManSection>
+  <Oper Name="KnightsGraph" Arg="[filt, ]m, n"/>
+  <Returns>A digraph.</Returns>
+  <Description>
+    If <A>m</A> and <A>n</A> are both positive integers, then this operation
+    returns the <E>Knight's Graph</E> for a <A>m</A> by <A>n</A> board. <P/>
+
+    From
+    <URL>https://en.wikipedia.org/wiki/Knight%27s_graph</URL>:
+    <P/>
+
+    <Q>In graph theory, a knight's graph, or a knight's tour graph, is a
+    graph that represents all legal moves of the knight chess piece on a
+    chessboard.  Each vertex of this graph represents a square of the
+    chessboard, and each edge connects two squares that are a knight's move
+    apart from each other. More specifically, an <A>m</A> by <A>n</A> knight's
+    graph is a knight's graph of an <A>m</A> by <A>n</A> chessboard.</Q>
+    <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> D := KnightsGraph(8, 8);
+<immutable connected symmetric digraph with 64 vertices, 336 edges>
+gap> IsConnectedDigraph(D);
+true
+gap> D := KnightsGraph(3, 3);
+<immutable symmetric digraph with 9 vertices, 16 edges>
+gap> IsConnectedDigraph(D);
+false
+gap> KnightsGraph(IsMutable, 3, 9);
+<mutable digraph with 27 vertices, 88 edges>
+]]></Example>
+  </Description>
+</ManSection>
+<#/GAPDoc>

doc/z-chap2.xml

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

gap/examples.gd

@@ -52,3 +52,7 @@ DeclareOperation("GeneralisedPetersenGraph", [IsFunction, IsInt, IsInt]);
 DeclareConstructor("StarDigraphCons", [IsDigraph, IsPosInt]);
 DeclareOperation("StarDigraph", [IsPosInt]);
 DeclareOperation("StarDigraph", [IsFunction, IsPosInt]);
+
+DeclareConstructor("KnightsGraphCons", [IsDigraph, IsPosInt, IsPosInt]);
+DeclareOperation("KnightsGraph", [IsPosInt, IsPosInt]);
+DeclareOperation("KnightsGraph", [IsFunction, IsPosInt, IsPosInt]);

gap/examples.gi

@@ -400,3 +400,49 @@ function(filt, k)
   SetIsCompleteBipartiteDigraph(D, k > 1);
   return D;
 end);
+
+InstallMethod(KnightsGraphCons,
+"for IsMutableDigraph and two positive integers",
+[IsMutableDigraph, IsPosInt, IsPosInt],
+function(filt, m, n)
+  local D, moveOffSets, coordinates, target, i, j, iPos;
+  D := EmptyDigraph(IsMutableDigraph, m * n);
+  moveOffSets := [[2, 1], [-2, 1], [2, -1], [-2, -1],
+  [1, 2], [-1, 2], [1, -2], [-1, -2]];
+  coordinates := [];
+  for i in [1 .. n] do
+    for j in [1 .. m] do
+      Add(coordinates, [i, j]);
+    od;
+  od;
+  iPos := 0;
+  for i in coordinates do
+    iPos := iPos + 1;
+    for j in moveOffSets do
+      target := [i[1] + j[1], i[2] + j[2]];
+      if target[1] in [1 .. n] and target[2] in [1 .. m] then
+        DigraphAddEdge(D, [iPos, (target[1] - 1) * m + target[2]]);
+      fi;
+    od;
+  od;
+  return D;
+end);
+
+InstallMethod(KnightsGraphCons,
+"for IsImmutableDigraph and two positive integers",
+[IsImmutableDigraph, IsPosInt, IsPosInt],
+function(filt, m, n)
+  local D;
+  D := MakeImmutable(KnightsGraphCons(IsMutableDigraph, m, n));
+  SetIsMultiDigraph(D, false);
+  SetIsSymmetricDigraph(D, true);
+  SetIsConnectedDigraph(D, m > 2 and n > 2 and not (m = 3 and n = 3));
+  return D;
+end);
+
+InstallMethod(KnightsGraph, "for a function and two positive integers",
+[IsFunction, IsPosInt, IsPosInt],
+KnightsGraphCons);
+
+InstallMethod(KnightsGraph, "for two positive integers", [IsPosInt, IsPosInt],
+{m, n} -> KnightsGraphCons(IsImmutableDigraph, m, n));

tst/standard/examples.tst

@@ -240,6 +240,18 @@ true
 gap> IsMultiDigraph(StarDigraph(3));
 false
 
+#  Knight's Graph
+gap> D := KnightsGraph(8, 8);
+<immutable connected symmetric digraph with 64 vertices, 336 edges>
+gap> IsConnectedDigraph(D);
+true
+gap> D := KnightsGraph(3, 3);
+<immutable symmetric digraph with 9 vertices, 16 edges>
+gap> IsConnectedDigraph(D);
+false
+gap> KnightsGraph(IsMutable, 3, 9);
+<mutable digraph with 27 vertices, 88 edges>
+
 #
 gap> DIGRAPHS_StopTest();
 gap> STOP_TEST("Digraphs package: standard/examples.tst", 0);