A graph consists of vertices and edges specifying a relation between any two vertices. A simple graph allows only one edge between vertices. Coloring the vertices has applications to scheduling problems. The chromatic polynomial of a graph is a one variable polynomial which encodes the number of ways to color a graph with a given number of colors. In the mid-1990s Stanley introduced a multivariable polynomial that generalizes the classic one variable chromatic polynomial. What properties of a graph can be recovered from this polynomial? A tree is a connected graph without cycles. It is conjectured that Stanley's polynomial distinguishes trees up to isomorphism. In this talk, I will discuss some recent results on this conjecture, some obtained by undergraduate students.
Copyright. All Rights Reserved.