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Add GeneralisedPetersenGraph function #204

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Jun 21, 2019
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Add GeneralisedPetersenGraph function #204

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195f319
Add GeneralisedPetersenGraph function
Jun 14, 2019
01ee47a
Modify construction to make output work more nicely with DigraphVerte…
Jun 14, 2019
64040fc
Implement changes
Jun 14, 2019
c6ca07a
Shorten tests
Jun 14, 2019
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27 changes: 27 additions & 0 deletions doc/exmpl.xml
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Expand Up @@ -26,6 +26,33 @@ gap> ChromaticNumber(PetersenGraph());
</ManSection>
<#/GAPDoc>

<#GAPDoc Label="GeneralisedPetersenGraph">
<ManSection>
<Attr Name="GeneralisedPetersenGraph" Arg="n, k"/>
<Returns>A digaph.</Returns>
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digaph -> digraph

<Description>
If <A>n</A> is a positive integer and <A>k</A> is a non-negative integer less than <A>n / 2</A>, then this operation returns the <E>Generalised Petersen Graph</E> <M>GPG(n, k)</M>. <P/>

From Wikipedia: The generalized Petersen graphs are a family of cubic graphs formed by connecting the vertices of a regular polygon to the corresponding vertices of a star polygon. They include the Petersen graph and generalize one of the ways of constructing the Petersen graph. The generalized Petersen graph family was introduced in 1950 by H. S. M. Coxeter and was given its name in 1969 by Mark Watkins.<P/>

For more information, see <URL>https://en.wikipedia.org/wiki/Generalized_Petersen_graph</URL><P/>

See also <Ref Func="DigraphsTestInstall"/>.
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Why do we see also DigraphsTestInstall??


<Example><![CDATA[
gap> GeneralisedPetersenGraph(7, 2);
<immutable digraph with 14 vertices, 42 edges>
gap> GeneralisedPetersenGraph(40, 1);
<immutable digraph with 80 vertices, 240 edges>
gap> D := GeneralisedPetersenGraph(5, 2);
<immutable digraph with 10 vertices, 30 edges>
gap> IsIsomorphicDigraph(D, PetersenGraph());
true
]]></Example>
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Why not add an example which returns a mutable digraph? Other manual examples don't do this only because they haven't yet been updated.

</Description>
</ManSection>
<#/GAPDoc>

<#GAPDoc Label="JohnsonDigraph">
<ManSection>
<Oper Name="JohnsonDigraph" Arg="n, k"/>
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1 change: 1 addition & 0 deletions doc/z-chap2.xml
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Expand Up @@ -77,6 +77,7 @@
<#Include Label="EmptyDigraph">
<#Include Label="JohnsonDigraph">
<#Include Label="PetersenGraph">
<#Include Label="GeneralisedPetersenGraph">
</Section>

</Chapter>
4 changes: 4 additions & 0 deletions gap/exmpl.gd
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Expand Up @@ -44,3 +44,7 @@ DeclareOperation("JohnsonDigraph", [IsFunction, IsInt, IsInt]);
DeclareConstructor("PetersenGraphCons", [IsDigraph]);
DeclareOperation("PetersenGraph", []);
DeclareOperation("PetersenGraph", [IsFunction]);

DeclareConstructor("GeneralisedPetersenGraphCons", [IsDigraph, IsInt, IsInt]);
DeclareOperation("GeneralisedPetersenGraph", [IsInt, IsInt]);
DeclareOperation("GeneralisedPetersenGraph", [IsFunction, IsInt, IsInt]);
57 changes: 57 additions & 0 deletions gap/exmpl.gi
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Expand Up @@ -356,3 +356,60 @@ InstallMethod(PetersenGraph, [],
function()
return PetersenGraphCons(IsImmutableDigraph);
end);

InstallMethod(GeneralisedPetersenGraphCons,
"for IsMutableDigraph, integer, integer",
[IsMutableDigraph, IsInt, IsInt],
function(filt, n, k)
local D, i;
if n < 1 then
ErrorNoReturn("the argument <n> must be a positive integer,");
elif k < 0 then
ErrorNoReturn("the argument <k> must be a non-negative integer,");
elif k > n / 2 then
ErrorNoReturn("the argument <k> must be less than <n> / 2,");
fi;
D := Digraph(filt, []);
for i in [1 .. n] do
DigraphAddVertex(D, i);
DigraphAddVertex(D, n + 1 + i);
od;
for i in [1 .. n] do
if i <> n then
DigraphAddEdge(D, [i, i + 1]);
else
DigraphAddEdge(D, [n, 1]);
fi;
DigraphAddEdge(D, [i, n + i]);
if n + i + k <= 2 * n then
DigraphAddEdge(D, [n + i, n + i + k]);
else
DigraphAddEdge(D, [n + i, (n + i + k) mod n + n]);
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Maybe some brackets around ((n + i + k) mod n) + n?

fi;
od;
DigraphSymmetricClosure(D);
return D;
end);

InstallMethod(GeneralisedPetersenGraphCons,
"for IsImmutableDigraph, integer, int",
[IsImmutableDigraph, IsInt, IsInt],
function(filt, n, k)
local D;
D := MakeImmutableDigraph(GeneralisedPetersenGraphCons(
IsMutableDigraph, n, k));
SetIsMultiDigraph(D, false);
SetIsSymmetricDigraph(D, true);
return D;
end);

InstallMethod(GeneralisedPetersenGraph, "for a function, integer, integer",
[IsFunction, IsInt, IsInt],
function(func, n, k)
return GeneralisedPetersenGraphCons(func, n, k);
end);

InstallMethod(GeneralisedPetersenGraph, "for integer, integer", [IsInt, IsInt],
function(n, k)
return GeneralisedPetersenGraphCons(IsImmutableDigraph, n, k);
end);
44 changes: 44 additions & 0 deletions tst/standard/exmpl.tst
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Expand Up @@ -21,6 +21,50 @@ gap> DigraphGirth(PetersenGraph());
gap> PetersenGraph(IsMutableDigraph);
<mutable digraph with 10 vertices, 30 edges>

# GeneralisedPetersenGraph
gap> D := GeneralisedPetersenGraph(8, 3);
<immutable digraph with 16 vertices, 48 edges>
gap> IsBipartiteDigraph(D);
true
gap> D := GeneralisedPetersenGraph(15, 7);
<immutable digraph with 30 vertices, 90 edges>
gap> IsBipartiteDigraph(D);
false
gap> D := GeneralisedPetersenGraph(10, 2);
<immutable digraph with 20 vertices, 60 edges>
gap> IsVertexTransitive(D);
true
gap> D := GeneralisedPetersenGraph(11, 2);
<immutable digraph with 22 vertices, 66 edges>
gap> IsVertexTransitive(D);
false
gap> D := GeneralisedPetersenGraph(5, 2);
<immutable digraph with 10 vertices, 30 edges>
gap> IsIsomorphicDigraph(D, PetersenGraph());
true
gap> mat8_3 := [[0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
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You could make this all much shorter by just doing:

gap> G8_3 := DigraphFromGraph6String("OCQa`Q?OH?a@A@@?_OGB@");

> [0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0],
> [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0],
> [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0],
> [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0],
> [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
> [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
> [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
> [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1],
> [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0],
> [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0],
> [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0],
> [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0],
> [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0],
> [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1],
> [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0]];;
gap> G8_3 := DigraphByAdjacencyMatrix(mat8_3);
<immutable digraph with 16 vertices, 48 edges>
gap> D := GeneralisedPetersenGraph(8, 3);
<immutable digraph with 16 vertices, 48 edges>
gap> IsIsomorphicDigraph(D, G8_3);
true

# CompleteDigraph
gap> gr := CompleteDigraph(5);
<immutable digraph with 5 vertices, 20 edges>
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