The Kneser chromatic function distinguishes trees

Abstract

R.P. Stanley defined an invariant for graphs called the chromatic symmetric function and conjectured it is a complete invariant for trees. Miezaki et al. generalized the chromatic symmetric function and defined the Kneser chromatic functions denoted by ${\left\{X_{K_{N,k}}\right\}}_{k\in N}$, and rephrase Stanley's conjecture that $X_{K_{N,1}}$ is a complete invariant for trees. This paper shows $X_{K_{N,2}}$ is a complete invariant for trees.