# A Few More Trees the Chromatic Symmetric Function Can Distinguish

## TL;DR

This paper extends the class of trees for which Stanley's chromatic symmetric function can distinguish non-isomorphic trees, verifying the conjecture for a broader class called 2-spiders.

## Contribution

It generalizes the class of spiders to n-spiders and proves the chromatic symmetric function distinguishes these trees for n=2.

## Key findings

- Chromatic symmetric function distinguishes 2-spiders.
- Verification of Stanley's conjecture for a new class of trees.

## Abstract

A well-known open problem in graph theory asks whether Stanley's chromatic symmetric function, a generalization of the chromatic polynomial of a graph, distinguishes between any two non-isomorphic trees. Previous work has proven the conjecture for a class of trees called spiders. This paper generalizes the class of spiders to $n$-spiders, where normal spiders correspond to $n = 1$, and verifies the conjecture for $n = 2$.