1998/12/11 by F. Y. Wu, C. King, W. T. Lu
Physics and Astronomy · #cond-mat.stat-mech
published as Ann. Inst. Fourier (Grenoble) 49, 1103-1114 (1999). · plain latex, 14 pages, 2 figs., to appear in Annales de l'Institut Fourier (1999)
arxiv created 1998/12/11 · arxiv updated 2009/11/30
The Tutte polynomial is a generalization of the chromatic polynomial of graph colorings. Here we present an extension called the rooted Tutte polynomial, which is defined on a graph where one or more vertices are colored with prescribed colors. We establish a number of results pertaining to the rooted Tutte polynomial, including a duality relation in the case that all roots reside around a single face of a planar graph. The connection with the Potts model is also reviewed.