Theta-0 Graph

Author

Eric W. Weisstein
April 14, 2007

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GraphTheory/Theta-0Graph.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Theta-0Graph.html.

©2007 Wolfram Research, Inc. except for portions noted otherwise

Plot

ShowGraph[Theta0,
AspectRatio->Automatic,
VertexColor->Red,
VertexStyle->Disk[.04]]

Properties

Through[{V,M}[Theta0]]

ChromaticPolynomial[Theta0,z]//TraditionalForm

ChromaticNumber[Theta0]

HamiltonianQ[Theta0]

BiconnectedQ[Theta0]

ConnectedComponents[Theta0]

BipartiteQ[Theta0]

Spectrum[Theta0]//SpectrumForm//TraditionalForm

Construction

Theta0:=AddEdges[ChangeVertices[GraphUnion[Cycle[6],EmptyGraph[1]],Join[First/@CircularEmbedding[6],{{0,0}}]],{{3,7},{7,6}}]