A graph polynomial from chromatic symmetric functions

Abstract

AbstractMany graph polynomials may be derived from the coefficients of the chromatic symmetric function of a graph when expressed in different bases. For instance, the chromatic polynomial is obtained by mapping for each in this function, while a polynomial whose coefficients enumerate acyclic orientations is obtained by mapping for each . In this paper, we study a new polynomial we call the tree polynomial arising by mapping , where is the chromatic symmetric function of a path with vertices. In particular, we show that this polynomial has a deletion‐contraction relation and has properties closely related to the chromatic polynomial while having coefficients that enumerate certain spanning trees and edge cutsets.