Multigraph

Author

Eric W. Weisstein
June 2, 2004

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

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

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<DiscreteMath`Combinatorica`

?PairGroupIndex

Figures

<<GraphColoring`

SimpleGraph[g_MultiGraph]:=Graph[Replace[#,l_List:>1,2]&/@g[[1]],g[[2]]]

g

ShowGraph[g]

ShowGraph[SimpleGraph[g]]

ShowGraph[MultiGraphToGraph[g]]

Generating Functions

SymmetricGroup[3]

PairGroupIndex[SymmetricGroup[3],x]

?PairGroup

PairGroup[SymmetricGroup[3]]

Table[CycleIndex[PairGroup[SymmetricGroup[n]],x],
{n,6}]/.x[n_]:>Subscript[x,n]//ColumnForm//TraditionalForm

Table[Expand[n! CycleIndex[PairGroup[SymmetricGroup[n]],x]],
{n,6}]/.x[n_]:>Subscript[x,n]//ColumnForm//TraditionalForm

Table[Expand[n! CycleIndex[PairGroup[SymmetricGroup[n]],x]],
{n,6}]/.x[n_]:>1/(1-x)

Series[(2/(1-x)),{x,0,10}]

Series[(1/(((1-x))^3))+(3/(((1-x))^2))+(2/(1-x)),{x,0,10}]