Zeros of Jones Polynomials of Graphs

Zeros of Jones Polynomials of Graphs

In this paper, we introduce the Jones polynomial of a graph G = (V,E) with k components as the following specialization of the Tutte polynomial: JG(t) = (−1)|V |−kt|E|−|V TG(−t,−t). We first study its basic properties and determine certain extreme coefficients. Then we prove that (−∞, 0] is a zero-free interval of Jones polynomials of connected bridgeless graphs while for any small > 0 or large...

Zeros of Jones Polynomials for Families of Knots and Links

We calculate Jones polynomials VL(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 ...

Some compact generalization of inequalities for polynomials with prescribed zeros

‎Let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial‎ ‎of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$‎. ‎In this paper we obtain some new results about the dependence of $|p(Rz)|$ on $|p(rz)| $ for $r^2leq rRleq k^2$‎, ‎$k^2 leq rRleq R^2$ and for $Rleq r leq k$‎. ‎Our results refine and generalize certain well-known polynomial inequalities‎.

Tutte Polynomials of Flower Graphs

Zeros of Chromatic and Flow Polynomials of Graphs

We survey results and conjectures concerning the zero distribution of chromatic and flow polynomials of graphs, and characteristic polynomials of matroids.