An Index of a Graph with Applications to Knot Theory

Presents the application of graph theory to knot theory. This book evaluates the braid index for many knots and links using the generalized Jones polynomial and the index of a graph, a fresh invariant introduced here. It is of interest to computer scientists.

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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.