GroupTheory`
GroupTheory`

GTCayleyGraph

GTCayleyGraph[group]

plots the Cayley graph of a point group.

Details and Options

  • The Cayley graph describes the structure of the group. The connection of the group elements mediated by the generators is graphically represented.
  • The command handles the crystallographic point groups.
  • The following options can be given:
  • GOVerbose FalseDecides if additional information is given.
    GOColorScheme {Blue,Red,Green}graphical representation of edges and vertices.
    GOPlot TrueDecides if the graph is plotted
    VertexSize 0.8size of the vertices
    VertexLabelStyle Directive[Blue, 15]style of the vertex labels
    VertexShapeFunction "Circle"shape of vertices
  • This command is not explained in:
  • W. Hergert, M.Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 4.1.2

Examples

open allclose all

Basic Examples  (1)

Plot the CayleyGraph for the group C4v.

Options  (6)

GOVerbose  (1)

More information is given with GOVerbose-> True . The matrix represents the edges of the graph.

GOColorScheme  (1)

The standard setting for the generator colors is {Blue, Red,Green}. If more than 3 generators appear you have to define more colors.

GOPlot  (1)

With GOPlot->False the graph is given in a standard form . It can be presented afterwards with Mathematica's graph tools, but the labeling with the symmetry elements is not provided.

VertexSize  (1)

The vertex size can be modified with respect tot the size of the graph.

VertexLabelStyle  (1)

The label style can be customized:

VertexShapeFunction  (1)

You can choose another shape of the vertices