Singleton Graph

Author

Eric W. Weisstein
September 16, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GraphTheory/SingletonGraph.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/SingletonGraph.html.

©2006 Wolfram Research, Inc. except for portions noted otherwise

Graph

ShowGraph[SingletonGraph]

Boxed Picture

Show[Graphics[{
Line[{{-1,-1},{1,-1},{1,1},{-1,1},{-1,-1}}/2],
PointSize[.04],Red,Point[{0,0}]
}],AspectRatio->Automatic]

Memberships

Misses Cage, DistanceRegular, Moore, RegularPolychoron, UnitDistance

p={ArchimedeanQ,BicolorableQ,BiconnectedQ,BicubicQ,BipartiteQ,CirculantGraphQ,Class1Q,Class2Q,ClawFreeQ,CompleteQ,CompleteBipartiteQ,CompletelyRegularQ,CubicQ,CycleQ,EdgeTransitiveQ,EulerianQ,HamiltonConnectedQ,HamiltonianQ,HypohamiltonianQ,HypotraceableQ,IdentityGraphQ,IntegralGraphQ,PerfectQ,PlanarQ,PlatonicQ,PolyhedralQ,QuarticQ,QuinticQ,RegularQ,SelfComplementaryQ,SemisymmetricQ,SnarkQ,SquareFreeGraphQ,StarQ,StronglyRegularQ,SymmetricGraphQ,TraceableQ,TreeQ,TriangleFreeGraphQ,VertexTransitiveQ,WeaklyRegularQ,WheelQ};
g=Through[p[SingletonGraph]]

Select[p,#[SingletonGraph]&]

Properties

Through[{V,M}[SingletonGraph]]

Through[{Diameter,Girth,Radius}[SingletonGraph]]//Timing

Automorphisms[SingletonGraph]//Timing

Spectrum[SingletonGraph]

{First[#],Length[#]}&/@Split[DegreeSequence[SingletonGraph]]

<<DiscreteMath`GraphPlot`

PseudoDiameter[SingletonGraph]

Through[{ChromaticNumber,EdgeConnectivity,VertexConnectivity}[SingletonGraph]]//Timing

ChromaticPolynomial[SingletonGraph,z]

EdgeChromaticNumber[SingletonGraph]//Timing