# THE BOUNDARIES OF DIPOLE GRAPHS AND THE COMPLETE BIPARTITE GRAPHS K2,n

• Kim, Dongseok
• Accepted : 2014.04.11
• Published : 2014.06.25
• 62 11

#### Abstract

We study the Seifert surfaces of a link by relating the embeddings of graphs with 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 $4^2_1$ and $5_2$.

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#### Cited by

1. The complete list of prime knots whose flat plumbing basket numbers are 6 or less vol.24, pp.07, 2015, https://doi.org/10.1142/S021821651550042X
2. THE BASKET NUMBERS OF KNOTS vol.23, pp.1, 2015, https://doi.org/10.11568/kjm.2015.23.1.115

#### Acknowledgement

Supported by : Kyonggi University