Knots and graphs
type: Item
instance of: scholarly article
title: Knots and graphs
zbMATH Open document ID: 0935.57006
DOI: 10.1016/S0960-0779(97)00096-9
author: B. I. Kurpita
author: K. Murasugi
published in: Chaos, Solitons and Fractals
publication date: 2000-05-03T00:00:00Z
review text: This paper is an exposition of relatively recent results concerning the interplay between graph and knot theory. The authors start with two specific graphs (the knot graph used by Bankwitz, the Seifert graph) extracted from a knot or link diagram and present two invariants of a graph (the polynomial of a signed graph, the cycle index) and some of their properties, and then look at how these two graph invariants can be used to calculate the braid index of an oriented link (especially a \(2\)-bridge knot and an alternating knot) and the minimum crossing number of an alternating link and a torus knot, together with several examples. In particular, this paper contains two conjectures which can be found in another expository article [\textit{K.Murasugi}, Sugaku Expo. 9, No. 2, 187-205 (1996); translation from Sugaku 46, No. 2, 91-111 (1994; Zbl 0867.57008)]. The paper will be of value to researchers in this field, as a concise introduction to many results and their relevant works.
reviewed by: Sang Youl Lee
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 57-02
Mathematics Subject Classification ID: 57M15
zbMATH DE Number: 1370405
zbMATH Keywords: link
zbMATH Keywords: cycle index
zbMATH Keywords: graph polynomial
zbMATH Keywords: braid index
zbMATH Keywords: minimum crossing number
zbMATH Keywords: skein polynomial
zbMATH Keywords: Jones polynomial
MaRDI profile type: Publication
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full work available at URL: s0960-0779(97)00096-9
OpenAlex ID: W2072084214
description: scientific article; zbMATH DE number 1370405