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In this paper, we present a formula for computing the Tutte polynomial of the signed graph formed from a labeled graph by edge replacements in terms of the chain polynomial of the labeled graph. Then we define a family of 'ring of tangles' links and consider zeros of their Jones polynomials. By applying the formula obtained, Beraha-Kahane-Weiss's theorem… (More)

Let G be a connected plane graph, D(G) be the corresponding link diagram via medial construction, and µ(D(G)) be the number of components of the link diagram D(G). In this paper, we first provide an elementary proof that µ(D(G)) ≤ n(G) + 1, where n(G) is the nullity of G. Then we lay emphasis on the extremal graphs, i.e. the graphs with µ(D(G)) = n(G) + 1.… (More)

The goal of this paper is to determine the braid index of two types of complicated DNA polyhedral links introduced by chemists and biologists in recent years. We shall study it in a more broad context and actually consider so-called Jaeger's links (more general Traldi's links) which contain, as special cases, both four types of simple polyhedral links whose… (More)

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: J G (t) = (−1) |V |−k t |E|−|V |+k T G (−t, −t −1). 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… (More)

In the last 20 years or so, chemists and molecular biologists have synthesized some novel DNA polyhedra. Polyhedral links were introduced to model DNA polyhedra and study topological properties of DNA polyhedra. As a very powerful invariant of oriented links, the Homfly polynomial of some of such polyhedral links with small number of crossings has been… (More)

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