networks(deprecated)/tuttepoly - Maple Help

networks

 tuttepoly
 Tutte polynomial of an undirected graph

 Calling Sequence tuttepoly(G, t, z)

Parameters

 G - undirected graph or network t - internal activity variable in Tutte poly z - external activity variable in Tutte poly

Description

 • Important: The networks package has been deprecated.Use the superseding command GraphTheory[TuttePolynomial] instead.
 • The Tutte polynomial is a sum over all maximal forests H of G of ${t}^{\mathrm{ia}\left(H\right)}{z}^{\mathrm{ea}\left(H\right)}$ where $\mathrm{ia}\left(H\right)$ is the internal activity of H and $\mathrm{ea}\left(H\right)$ is the external activity of H.
 • This routine is normally loaded via the command with(networks) but may also be referenced using the full name networks[tuttepoly](...).

Examples

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

 > $\mathrm{with}\left(\mathrm{networks}\right):$
 > $G≔\mathrm{complete}\left(4\right):$
 > $\mathrm{tuttepoly}\left(G,t,z\right)$
 ${{t}}^{{3}}{+}{{z}}^{{3}}{+}{3}{}{{t}}^{{2}}{+}{4}{}{t}{}{z}{+}{3}{}{{z}}^{{2}}{+}{2}{}{t}{+}{2}{}{z}$ (1)
 > $\mathrm{tuttepoly}\left(G,2,2\right)$
 ${64}$ (2)
 > $\mathrm{tuttepoly}\left(G,2,1\right)$
 ${38}$ (3)
 > $\mathrm{tuttepoly}\left(G,1,2\right)$
 ${38}$ (4)
 > $\mathrm{tuttepoly}\left(G,1,1\right)$
 ${16}$ (5)