tutte

Tutte polynomial for planar graphs represented as PlanarDiagram objects.

This computes the Tutte polynomial T(_x, _y) for planar graphs (no crossings) using the standard deletion–contraction recursion until only loops and bridges remain, where each terminal graph contributes _x^(#bridges) * _y^(#loops).

Functions

deletion_contraction(k, *[, contract_bridges])	Return terminal diagrams after recursive deletion–contraction.
tutte(k)	Compute the Tutte polynomial T(_x, _y) of a planar graph (no crossings).

tutte(k)

Compute the Tutte polynomial T(_x, _y) of a planar graph (no crossings).

Parameters:

k (PlanarDiagram | OrientedPlanarDiagram) – Planar diagram representing a planar graph (unoriented or oriented).

Returns:

SymPy expression T(_x, _y).

Raises:

ValueError – If k is not a planar graph (contains crossings).

Return type:

Expr