This book presents a remarkable application of graph theory to knot theory. In knot theory, there are a number of easily defined geometric invariants that are extremely difficult to compute; the braid index of a knot or link is one example. The authors evaluate the braid index for many knots and links using the generalized Jones polynomial and the index of a graph, a new invariant introduced here. This invariant, which is determined algorithmically, is likely to be of particular interest to computer scientists.

Readership

Specialists and graduate students interested in combinatorial knot theory and/or graph theory.

Table of Contents

• Index of a graph
• Link theory
• Braid index of alternating links
• Appendix
• References