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Combinatorics

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  • Combinatorics

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  • Functions I understand in combinatorics

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  • Combinatorics
  • Stirling permutation

Symbols

  • CanonicalMultiset
  • CentralBinomialCoefficient
  • ConjugatePartition
  • DescendingSublists
  • DivisorHasseDiagram
  • DominatingIntegerPartitionQ
  • DurfeeSquare
  • EnumerateMultisetPartialDerangements
  • EulerianCatalanNumber
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  • EulerianNumberOfTheSecondKind
  • FerrersDiagram
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  • FibonacciEncode
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  • FrobeniusSymbolFromPartition
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  • GaussFactorial
  • GrayCode
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  • HuffmanCodeWords
  • HuffmanDecode
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  • IntegerPartitionQ
  • InverseFibonacci
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  • InversionCount
  • InversionVectorQ
  • LehmerCodeFromPermutation
  • LucasNumberU1
  • LucasNumberV2
  • ModifiedCentralBinomialCoefficient
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  • PartialOrderGraphQ
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  • ReflexiveGraphQ
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PeterBurbery`Combinatorics`
ReflexiveGraphQ
​
ReflexiveGraphQ
[g]
yields
True
if the graph
g
is reflexive and
False
otherwise.
​
Details and Options

Examples  
(2)
Basic Examples  
(2)
Tuples form a reflexive graph:
In[1]:=
Tuples[CharacterRange["a","e"],2]
Out[1]=
{{a,a},{a,b},{a,c},{a,d},{a,e},{b,a},{b,b},{b,c},{b,d},{b,e},{c,a},{c,b},{c,c},{c,d},{c,e},{d,a},{d,b},{d,c},{d,d},{d,e},{e,a},{e,b},{e,c},{e,d},{e,e}}
In[2]:=
g=Graph[UndirectedEdge@@@%]
Out[2]=
In[3]:=
ReflexiveGraphQ
[%]
Out[3]=
True
After deleting one of its self-loops, the graph is no longer reflexive:
In[4]:=
EdgeDelete[g,UndirectedEdge["d","d"]]
Out[4]=
In[5]:=
ReflexiveGraphQ
[%]
Out[5]=
False
​
The divisibility relation between integers is reflexive since each integer divides itself:
In[1]:=
g=RelationGraph[(Mod[#1,#2]0)&,Range[6],VertexLabels"Name"]
Out[1]=
In[2]:=
ReflexiveGraphQ
[%]
Out[2]=
True
SeeAlso
TransitiveGraphQ
 
▪
Graph
 
▪
PartialOrderGraphQ
RelatedGuides
▪
Combinatorics
RelatedLinks
ReflexiveGraphQ
Resource Function contributed by Wolfram Staff (original content by Sriram V. Pemmaraju and Steven S. Skiena)
""

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