The boundaries of dipole graphs and the complete bipartite graphs K_{2,n}

Abstract

We study the Seifert surfaces of a link by relating the embeddings of graphs by using induced graphs. As applications, we prove that every link $L$ is the boundary of an oriented surface which is obtained from a graph embedding of a complete bipartite graph $K_{2,n}$, where all voltage assignments on the edges of $K_{2,n}$ are 0. We also provide an algorithm to construct such a graph diagram of a given link and demonstrate the algorithm by dealing with the links $4_1^2$ and $5_2$.

14 pages, 12 figures

References in corpus (2)

• The Jones polynomial and graphs on surfaces
• Seifert surfaces in open books, and a new coding algorithm for links

Cited by in corpus (1)

• The complete list of prime knots whose flat plumbing basket numbers are 6 or less