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

• Kim, Dongseok (Department of Mathematics, Kyonggi University)
• Accepted : 2014.04.11
• Published : 2014.06.25
• 86 13

#### 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 $5_2$.

#### Acknowledgement

Supported by : Kyonggi University

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