Vol. 13, No. 1, 2020

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A few more trees the chromatic symmetric function can distinguish

Jake Huryn and Sergei Chmutov

Vol. 13 (2020), No. 1, 109–116
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 nonisomorphic 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 $n=2$.

Keywords
graph theory, combinatorics, chromatic symmetric function
Mathematical Subject Classification 2010
Primary: 05C05, 05C31, 05E05