A Vertex-Weighted Tutte Symmetric Function, and Constructing Graphs with Equal Chromatic Symmetric Function

José Aliste-Prieto; Logan Crew; Sophie Spirkl; José Zamora

A Vertex-Weighted Tutte Symmetric Function, and Constructing Graphs with Equal Chromatic Symmetric Function

Combinatorics 2021-10-04 v3

Authors: José Aliste-Prieto , Logan Crew , Sophie Spirkl , José Zamora

Abstract

This paper has two main parts. First, we consider the Tutte symmetric function $XB$ , a generalization of the chromatic symmetric function. We introduce a vertex-weighted version of $XB$ and show that this function admits a deletion-contraction relation. We also demonstrate that the vertex-weighted $XB$ admits spanning-tree and spanning-forest expansions generalizing those of the Tutte polynomial by connecting $XB$ 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.

Keywords

graph polynomials

Cite

@article{arxiv.2007.11042,
  title  = {A Vertex-Weighted Tutte Symmetric Function, and Constructing Graphs with Equal Chromatic Symmetric Function},
  author = {José Aliste-Prieto and Logan Crew and Sophie Spirkl and José Zamora},
  journal= {arXiv preprint arXiv:2007.11042},
  year   = {2021}
}

Comments

Accepted manuscript; link to journal version: https://www.combinatorics.org/ojs/index.php/eljc/article/view/v28i2p1

A Vertex-Weighted Tutte Symmetric Function, and Constructing Graphs with Equal Chromatic Symmetric Function

Abstract

Keywords

Cite

Comments

Related papers