Null Graph

Author

Eric W. Weisstein
September 16, 2006

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

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

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

Graph

ShowGraph[NullGraph]

Boxed Picture

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

Memberships

p={BicolorableQ,BiconnectedQ,BipartiteQ,CirculantGraphQ,ClawFreeQ,CompleteQ,CubicQ,CycleQ,EdgeTransitiveQ,EulerianQ,HamiltonianQ,HamiltonConnectedQ,IdentityGraphQ,IntegralGraphQ,PerfectQ,PlanarQ,PolyhedralQ,QuarticQ,QuinticQ,RegularQ,SelfComplementaryQ,SemisymmetricQ,SnarkQ,SquareFreeGraphQ,StarQ,SymmetricGraphQ,TraceableQ,TreeQ,TriangleFreeGraphQ,VertexTransitiveQ,WheelQ};
Through[p[NullGraph]]

Position[%%,{}]

p[[14]]

Select[p,#[NullGraph]&]

Properties

Through[{V,M}[NullGraph]]

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

Automorphisms[NullGraph]//Timing

Spectrum[NullGraph]

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

<<DiscreteMath`GraphPlot`

PseudoDiameter[NullGraph]

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

ChromaticPolynomial[NullGraph,z]

EdgeChromaticNumber[NullGraph]//Timing