Document Type

Article - Open Access

Publication Title

Journal of Knot Theory and Its Ramifications

Publication Date


Abstract/ Summary

A book representation of a graph is a particular way of embedding a graph in three dimensional space so that the vertices lie on a circle and the edges are chords on disjoint topological disks. We describe a set of operations on book representations that preserves ambient isotopy, and apply these operations to K6, the complete graph with six vertices. We prove there are exactly 59 distinct book representations for K6, and we identify the number and type of knotted and linked cycles in each representation. We show that book representations of K6 contain between one and seven links, and up to nine knotted cycles. Furthermore, all links and cycles in a book representation of K6 have crossing number at most four.



Author Manuscript

This is a pre-publication author manuscript of the final, published article.