A Vertex-Weighted Tutte Symmetric Function, and Constructing Graphs with Equal Chromatic Symmetric Function
arXiv:2007.11042
Abstract
This paper has two main parts. First, we consider the Tutte symmetric function , a generalization of the chromatic symmetric function. We introduce a vertex-weighted version of and show that this function admits a deletion-contraction relation. We also demonstrate that the vertex-weighted admits spanning-tree and spanning-forest expansions generalizing those of the Tutte polynomial by connecting to other graph functions. Second, we give several methods for constructing nonisomorphic graphs with equal chromatic and Tutte symmetric functions, and use them to provide specific examples.
Accepted manuscript; link to journal version: https://www.combinatorics.org/ojs/index.php/eljc/article/view/v28i2p1