Abstract
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 V L ( 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.
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