Zeros of Jones polynomials for families of knots and links

We calculate Jones polynomials V-L(t) for several families of alternating knots and links, by, computing the Tutte polynomials T(G, x, y) for the associated graphs G and then obtaining VL(t) as a special case of the Tutte polynomial. For each of these families we determine the zeros of the Jones. polynomial, including the accumulation set in the limit of infinitely many crossings. A discussion is also, given of the calculation of Jones polynomials for non-alternating links. (C) 2001 Elsevier Science B.V. All rights reserved.