A Graph Polynomial from Chromatic Symmetric Functions

TL;DR

This paper explores how various graph polynomials can be derived from chromatic symmetric functions and introduces a new polynomial based on expansions involving chromatic symmetric functions of trees.

Contribution

It reveals connections between graph polynomials and chromatic symmetric functions and introduces a novel polynomial from tree-based expansions.

Findings

Many known graph polynomials originate from chromatic symmetric function coefficients.

A new polynomial is introduced based on expansions over chromatic symmetric functions of trees.

The study enhances understanding of the relationship between graph polynomials and symmetric functions.

Abstract

This paper describes how many known graph polynomials arise from the coefficients of chromatic symmetric function expansions in different bases, and studies a new polynomial arising by expanding over a basis given by chromatic symmetric functions of trees.