Symmetric function generalizations of graph polynomials

Abstract

In Chapter 2 we study the path-cycle symmetric function of a digraph, a symmetric function generalization of Chung and Graham's cover polynomial. Most of this material appears in either Advances in Math. 118 (1996), 71-98 or J. Algebraic Combin. 10 (1999), 227-240. Chapter 3 contains miscellaneous results about Stanley's symmetric function generalization X_G of the chromatic polynomial, e.g., we establish a connection with some of Tutte's work on the chromatic polynomial and use this to prove that X_G is reconstructible. Most of Chapter 3 does not appear elsewhere.