Add characteristic polynomial for a digraph (#164)

digraphs · Feb 15, 2019 · 422154c · 422154c
1 parent 3977137
commit 422154c
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Showing 5 changed files with 53 additions and 2 deletions.
diff --git a/doc/attr.xml b/doc/attr.xml
@@ -267,6 +267,33 @@ gap> Display(mat);
 </ManSection>
 <#/GAPDoc>
 
+<#GAPDoc Label="CharacteristicPolynomial">
+<ManSection>
+  <Attr Name="CharacteristicPolynomial" Arg="digraph"/>
+  <Returns>A polynomial with integer coefficients.</Returns>
+  <Description>
+    This function returns the characteristic polynomial of the digraph
+     <A>digraph</A>. That is it returns the characteristic polynomial
+      of the adjacency matrix of the digraph <A>digraph</A>
+    <Example><![CDATA[
+gap> gr := Digraph([
+> [2, 2, 2], [1, 3, 6, 8, 9, 10], [4, 6, 8],
+> [1, 2, 3, 9], [3, 3], [3, 5, 6, 10], [1, 2, 7],
+> [1, 2, 3, 10, 5, 6, 10], [1, 3, 4, 5, 8, 10],
+> [2, 3, 4, 6, 7, 10]]);
+<multidigraph with 10 vertices, 44 edges>
+gap> CharacteristicPolynomial(gr);
+x_1^10-3*x_1^9-7*x_1^8-x_1^7+14*x_1^6+x_1^5-26*x_1^4+51*x_1^3-10*x_1^2\
++18*x_1-30
+gap> gr := CompleteDigraph(5);
+<digraph with 5 vertices, 20 edges>
+gap> CharacteristicPolynomial(gr);
+x_1^5-10*x_1^3-20*x_1^2-15*x_1-4
+]]></Example>
+  </Description>
+</ManSection>
+<#/GAPDoc>
+
 <#GAPDoc Label="BooleanAdjacencyMatrix">
 <ManSection>
   <Attr Name="BooleanAdjacencyMatrix" Arg="digraph"/>

diff --git a/doc/z-chap4.xml b/doc/z-chap4.xml
@@ -19,6 +19,7 @@
 
   <Section><Heading>Neighbours and degree</Heading>
     <#Include Label="AdjacencyMatrix">
+    <#Include Label="CharacteristicPolynomial">
     <#Include Label="BooleanAdjacencyMatrix">
     <#Include Label="DigraphAdjacencyFunction">
     <#Include Label="RangeSourceDigraph">
@@ -61,7 +62,7 @@
     <#Include Label="DigraphDegeneracyOrdering">
     <#Include Label="HamiltonianPath">
   </Section>
-  
+
   <Section><Heading>Cayley graphs of groups</Heading>
     <#Include Label="GroupOfCayleyDigraph">
     <#Include Label="GeneratorsOfCayleyDigraph">
@@ -70,7 +71,7 @@
   <Section><Heading>Associated semigroups</Heading>
     <#Include Label="AsSemigroup">
   </Section>
-  
+
   <Section><Heading>Planarity</Heading>
     <#Include Label="KuratowskiPlanarSubdigraph">
     <#Include Label="KuratowskiOuterPlanarSubdigraph">

diff --git a/gap/attr.gd b/gap/attr.gd
@@ -57,6 +57,7 @@ DeclareAttribute("DigraphTransitiveClosure", IsDigraph);
 DeclareGlobalFunction("DigraphTransitiveClosureNC");
 
 DeclareAttribute("ChromaticNumber", IsDigraph);
+DeclareAttribute("CharacteristicPolynomial", IsDigraph);
 
 DeclareAttribute("DigraphAdjacencyFunction", IsDigraph);
 

diff --git a/gap/attr.gi b/gap/attr.gi
@@ -1530,3 +1530,10 @@ function(D)
   SetIsAntisymmetricDigraph(out, true);
   return out;
 end);
+
+InstallMethod(CharacteristicPolynomial,
+"for a digraph",
+[IsDigraph],
+function(gr)
+    return CharacteristicPolynomial(AdjacencyMatrix(gr));
+end);
diff --git a/tst/standard/attr.tst b/tst/standard/attr.tst
@@ -1706,6 +1706,21 @@ gap> OutNeighbours(last);
 gap> MaximalAntiSymmetricSubdigraph(CompleteDigraph(10));
 <digraph with 10 vertices, 45 edges>
 
+# CharacteristicPolynomial
+gap> gr := Digraph([
+> [2, 2, 2], [1, 3, 6, 8, 9, 10], [4, 6, 8],
+> [1, 2, 3, 9], [3, 3], [3, 5, 6, 10], [1, 2, 7],
+> [1, 2, 3, 10, 5, 6, 10], [1, 3, 4, 5, 8, 10],
+> [2, 3, 4, 6, 7, 10]]);
+<multidigraph with 10 vertices, 44 edges>
+gap> CharacteristicPolynomial(gr);
+x_1^10-3*x_1^9-7*x_1^8-x_1^7+14*x_1^6+x_1^5-26*x_1^4+51*x_1^3-10*x_1^2+18*x_1-\
+30
+gap> gr := CompleteDigraph(5);
+<digraph with 5 vertices, 20 edges>
+gap> CharacteristicPolynomial(gr);
+x_1^5-10*x_1^3-20*x_1^2-15*x_1-4
+
 #  DIGRAPHS_UnbindVariables
 gap> Unbind(adj);
 gap> Unbind(adj1);