Isomorphism of weighted trees and Stanley's isomorphism conjecture for caterpillars
Martin Loebl, Jean‐Sébastien Sereni · Annales de l’Institut Henri Poincaré D Combinatorics Physics and their Interactions · 2019
This paper contributes to a programme initiated by the first author: "How much information about a graph is revealed in its Potts partition function?“ We show that the W -polynomial distinguishes non-isomorphic weighted trees of a good family. The framework developed to do so also allows us to show that the W -polynomial distinguishes non-isomorphic caterpillars. This establishes Stanley's conjecture for caterpillars, an extensively studied problem.