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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)
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)
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