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](...).

$\mathrm{with}\left(\mathrm{networks}\right)\:$

$G≔\mathrm{complete}\left(4\right)\:$

$\mathrm{tuttepoly}\left(G\,t\,z\right)$

$t^3+z^3+3t^2+4tz+3z^2+2t+2z$

$\mathrm{tuttepoly}\left(G\,2\,2\right)$

$64$

$\mathrm{tuttepoly}\left(G\,2\,1\right)$

$38$

$\mathrm{tuttepoly}\left(G\,1\,2\right)$

$38$

$\mathrm{tuttepoly}\left(G\,1\,1\right)$

$16$