Zeros of the Jones polynomials for families of pretzel links

In this paper, a general method for computing the Tutte polynomial of the subdivision of a graph is explained. As an application to the subdivision of sheaf graph which consists of two vertices joined by some parallel edges, we obtain the explicit expressions of the Jones polynomials for some families of the pretzel links. Motivated by the work of Chang and Shrock, we investigate the zeros distribution of its Jones polynomial for each family when the number of crossings goes to infinity, and generalize some of their results. (C) 2003 Published by Elsevier B.V.