Generating functions of $q$-chromatic polynomials

Matthias Beck, Benjamin Braun, Alvaro Cornejo

Given a graph $G=(V,E)$ and a linear form $\lambda \in {\mathbb{Z}}_{>0}^V$, Bajo et al. (2025) introduced the $q$-chromatic polynomial ${\chi }_G^{\lambda }(q,n):=\sum q^{{\sum }_{v\in V}{\lambda }_{v}c(v)}$ w…