Dipyramidal Graph
Author
Eric W. Weisstein
Title
Dipyramidal Graph
Description
A n-dipyramidal graph is the skeleton of an n-sided dipyramid. It has vertex count n+2 and edge count 3n. The 3-dipyramidal graph is the unique graph K_5-e obtained by removing any single edge from the pentatope graph K_5. Special cases are summarized in the following table. n graph 3 12-Johnson skeleton graph 4 octahedral graph 5 32-Johnson skeleton graph
Category
Educational Materials
Keywords
URL
http://www.notebookarchive.org/2019-07-0z3v5c4/
DOI
https://notebookarchive.org/2019-07-0z3v5c4
Date Added
2019-07-02
Date Last Modified
2019-07-02
File Size
5.01 megabytes
Supplements
Rights
Redistribution rights reserved
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Dipyramidal Graph
Dipyramidal Graph
Author
Author
Eric W. Weisstein
July 2, 2018
July 2, 2018
This notebook downloaded from http://mathworld.wolfram.com/notebooks/GraphTheory/DipyramidalGraph.nb.
For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/DipyramidalGraph.html.
©2018 Wolfram Research, Inc. except for portions noted otherwise
Figure
Figure
Graphs.m
Graphs.m
In[]:=
GraphicsGrid[Partition[Table[Show[DipyramidalGraph[n]//StyleGraphs[#,VertexSize{"Scaled",.05}]&,PlotLabelStyle[HoldForm[n]n,FontFamily"Times"]],{n,3,10}],4],ImageSize400,DividersAll]
Out[]=
GraphData "Graph"
GraphData "Graph"
In[]:=
GraphicsGrid[Partition[Table[Show[GraphData[{"Dipyramid",n}]//StyleGraphs[#,VertexSize{"Scaled",.05}]&,PlotLabelStyle[HoldForm[n]n,FontFamily"Times"]],{n,3,10}],4],ImageSize400,DividersAll]
Out[]=
GraphData "3D"
GraphData "3D"
In[]:=
GraphicsGrid[Partition[Table[Show[GraphData[{"Dipyramid",n},"Graph","3D"]//StyleGraphs[#,VertexSize{"Scaled",.05}]&,PlotLabelStyle[HoldForm[n]n,FontFamily"Times"]],{n,3,10}],4],ImageSize400,DividersAll]
Out[]=
GraphData {"3D","UnitDistance"}
GraphData {"3D","UnitDistance"}
In[]:=
GraphicsGrid[Partition[Table[GraphData[{"Dipyramid",n},"Graph",{"3D","UnitDistance"}]/.{{}"",{g_System`Graph,___}:>Show[g//StyleGraphs[#,VertexSize{"Scaled",.05}]&,PlotLabelStyle[HoldForm[n]n,FontFamily"Times"]]},{n,3,10}],4],ImageSize400,DividersAll]
Out[]=
Special cases
Special cases
In[]:=
TextGrid[DeleteCases[Table[{n,rg=DipyramidalGraph[n]//RecognizeGraph},{n,3,20}],{_,{"Dipyramid",_}}],DividersAll]
Out[]=
4 | OctahedralGraph |
Construction
Construction
Properties
Properties
Acyclic
Acyclic
AdjacencyMatrixCount
AdjacencyMatrixCount
Anarboricity
Anarboricity
Arboricity
Arboricity
ArcTransitive
ArcTransitive
ArcTransitivity
ArcTransitivity
AutomorphismCount
AutomorphismCount
BalabanIndex
BalabanIndex
Bandwidth
Bandwidth
BridgeCount
BridgeCount
BurningNumber
BurningNumber
CharacteristicPolynomial
CharacteristicPolynomial
ChordCount
ChordCount
Chordless
Chordless
ChordlessCycleCount
ChordlessCycleCount
Chords
Chords
ChromaticInvariant
ChromaticInvariant
ChromaticNumber
ChromaticNumber
ChromaticPolynomial
ChromaticPolynomial
Circumference
Circumference
Classes
Classes
CliqueCount
CliqueCount
CliqueCoveringNumber
CliqueCoveringNumber
CliquePolynomial
CliquePolynomial
CliqueNumber
CliqueNumber
ComplementOddChordlessCycleCount
ComplementOddChordlessCycleCount
ConnectedDominatingSetCount
ConnectedDominatingSetCount
ConnectedDominationNumber
ConnectedDominationNumber
ConnectedDominationPolynomial
ConnectedDominationPolynomial
ConnectedInducedSubgraphCount
ConnectedInducedSubgraphCount
ConnectedInducedSubgraphPolynomial
ConnectedInducedSubgraphPolynomial
CrossingNumber
CrossingNumber
CycleCount
CycleCount
CyclePolynomial
CyclePolynomial
Cyclic
Cyclic
CyclomaticNumber
CyclomaticNumber
DetourIndex
DetourIndex
DetourPolynomial
DetourPolynomial
Diameter
Diameter
DistancePolynomial
DistancePolynomial
DistinguishingNumber
DistinguishingNumber
DomaticNumber
DomaticNumber
DominationNumber
DominationNumber
DominationPolynomial
DominationPolynomial
DominatingSetCount
DominatingSetCount
EdgeChromaticNumber
EdgeChromaticNumber
EdgeConnectivity
EdgeConnectivity
EdgeCount
EdgeCount
EdgeCoverCount
EdgeCoverCount
EdgeCoverNumber
EdgeCoverNumber
EdgeCoverPolynomial
EdgeCoverPolynomial
EulerianCycleCount
EulerianCycleCount
FaceCount
FaceCount
FlowPolynomial
FlowPolynomial
FractionalChromaticNumber
FractionalChromaticNumber
FractionalCliqueNumber
FractionalCliqueNumber
FractionalEdgeChromaticNumber
FractionalEdgeChromaticNumber
Girth
Girth
HamiltonDecompositionCount
HamiltonDecompositionCount
Hamiltonian
Hamiltonian
HamiltonianCycleCount
HamiltonianCycleCount
HamiltonianNumber
HamiltonianNumber
HamiltonianPathCount
HamiltonianPathCount
HamiltonianWalkCount
HamiltonianWalkCount
HararyIndex
HararyIndex
HexagonCount
HexagonCount
IdiosyncraticPolynomial
IdiosyncraticPolynomial
IndependenceNumber
IndependenceNumber
IndependencePolynomial
IndependencePolynomial
IndependenceRatio
IndependenceRatio
IndependentEdgeSetCount
IndependentEdgeSetCount
IndependentVertexSetCount
IndependentVertexSetCount
IntersectionNumber
IntersectionNumber
IrredundancePolynomial
IrredundancePolynomial
IrredundantSetCount
IrredundantSetCount
KirchhoffIndex
KirchhoffIndex
KirchhoffSumIndex
KirchhoffSumIndex
LaplacianPolynomial
LaplacianPolynomial
LeafCount
LeafCount
Likelihood
Likelihood
LongestCycleCount
LongestCycleCount
LongestPathLength
LongestPathLength
LongestPathCount
LongestPathCount
LovaszNumber
LovaszNumber
MatchingGeneratingPolynomial
MatchingGeneratingPolynomial
MatchingNumber
MatchingNumber
MatchingPolynomial
MatchingPolynomial
MaximalCliqueCount
MaximalCliqueCount
MaximalIndependentEdgeSetCount
MaximalIndependentEdgeSetCount
MaximalIndependentVertexSetCount
MaximalIndependentVertexSetCount
MaximalIrredundantSetCount
MaximalIrredundantSetCount
MaximumCliqueCount
MaximumCliqueCount
MaximumIndependentEdgeSetCount
MaximumIndependentEdgeSetCount
MaximumIndependentVertexSetCount
MaximumIndependentVertexSetCount
MaximumIrredundantSetCount
MaximumIrredundantSetCount
MaximumLeafNumber
MaximumLeafNumber
MaximumVertexDegree
MaximumVertexDegree
MeanDistance
MeanDistance
MinimalDominatingSetCount
MinimalDominatingSetCount
MinimalDominatingSetSignature
MinimalDominatingSetSignature
MinimalEdgeCoverCount
MinimalEdgeCoverCount
MinimalTotalDominatingSetCount
MinimalTotalDominatingSetCount
MinimumCoveringsByMaximalCliquesCount
MinimumCoveringsByMaximalCliquesCount
MinimumConnectedDominatingSetCount
MinimumConnectedDominatingSetCount
MinimumDistinguishingLabelingCount
MinimumDistinguishingLabelingCount
MinimumDominatingSetCount
MinimumDominatingSetCount
MinimumEdgeCoverCount
MinimumEdgeCoverCount
MinimumTotalDominatingSetCount
MinimumTotalDominatingSetCount
MinimumVertexCoverCount
MinimumVertexCoverCount
MinimumVertexDegree
MinimumVertexDegree
MolecularTopologicalIndex
MolecularTopologicalIndex
Nonhamiltonian
Nonhamiltonian
OddChordlessCycleCount
OddChordlessCycleCount
PathCount
PathCount
PathPolynomial
PathPolynomial
PentagonCount
PentagonCount
ProjectivePlaneCrossingNumber
ProjectivePlaneCrossingNumber
Radius
Radius
RankPolynomial
RankPolynomial
RectilinearCrossingNumber
RectilinearCrossingNumber
ReliabilityPolynomial
ReliabilityPolynomial
ShannonCapacity
ShannonCapacity
SigmaPolynomial
SigmaPolynomial
Skewness
Skewness
SpanningTreeCount
SpanningTreeCount
SquareCount
SquareCount
StabilityIndex
StabilityIndex
TopologicalIndex
TopologicalIndex
ToroidalCrossingNumber
ToroidalCrossingNumber
TotalDominatingSetCount
TotalDominatingSetCount
TotalDominationNumber
TotalDominationNumber
TotalDominationPolynomial
TotalDominationPolynomial
Traceable
Traceable
Triameter
Triameter
TriangleCount
TriangleCount
TuttePolynomial
TuttePolynomial
Untraceable
Untraceable
VertexConnectivity
VertexConnectivity
VertexCoverCount
VertexCoverCount
VertexCoverNumber
VertexCoverNumber
VertexCount
VertexCount
VertexCoverPolynomial
VertexCoverPolynomial
VertexDegrees
VertexDegrees
WienerIndex
WienerIndex
WienerSumIndex
WienerSumIndex
GraphData
GraphData
Cite this as: Eric W. Weisstein, "Dipyramidal Graph" from the Notebook Archive (2018), https://notebookarchive.org/2019-07-0z3v5c4
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