networks(deprecated)/chrompoly - Help

networks

 chrompoly
 chromatic polynomial of an undirected graph

 Calling Sequence chrompoly(G, lambda)

Parameters

 G - undirected graph or network lambda - variable in chromatic poly (usually number of colors)

Description

 • Important: The networks package has been deprecated.  Use the superseding command GraphTheory[ChromaticPolynomial] instead.
 • This routine returns the chromatic polynomial of the graph G as a polynomial in lambda.  The value of this polynomial gives the number of proper vertex-colorings of G using lambda colors.
 • The procedure is normally loaded via the command with(networks) but can also be referenced using the full name networks[chrompoly](...).

Examples

Important: The networks package has been deprecated.  Use the superseding command GraphTheory[ChromaticPolynomial] instead.

 > $\mathrm{with}\left(\mathrm{networks}\right):$
 > $G≔\mathrm{complete}\left(4\right):$
 > $\mathrm{chrompoly}\left(G,x\right)$
 ${x}{}\left({x}{-}{1}\right){}\left({x}{-}{2}\right){}\left({x}{-}{3}\right)$ (1)
 > $\mathrm{chrompoly}\left(G,3\right)$
 ${0}$ (2)
 > $\mathrm{chrompoly}\left(G,4\right)$
 ${24}$ (3)
 > $\mathrm{addedge}\left(\left\{\left\{1,2\right\},\left\{1,1\right\}\right\},G\right):$
 > $\mathrm{chrompoly}\left(G,x\right)$
 ${0}$ (4)