## Abstract

Since the Jones polynomial was discovered, the connection between knot theory and quantum physics has been of great interest. Lomonaco and Kauffman introduced the knot mosaic system to give a definition of the quantum knot system that is intended to represent an actual physical quantum system. Recently the authors developed an algorithm producing the exact enumeration of knot mosaics, which uses a recursion formula of state matrices. As a sequel to this research program, we similarly define the (embedded) graph mosaic system by using 16 graph mosaic tiles, representing graph diagrams with vertices of valence 3 and 4. We extend the algorithm to produce the exact number of all graph mosaics. The magnified state matrix that is an extension of the state matrix is mainly used.

Original language | English |
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Article number | 1750032 |

Journal | Journal of Knot Theory and its Ramifications |

Volume | 26 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2017 Apr 1 |

### Bibliographical note

Funding Information:The corresponding author(Seungsang Oh) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIP) (No. NRF-2014R1A2A1A11050999).

Publisher Copyright:

© 2017 World Scientific Publishing Company.

## Keywords

- Quantum knot
- graph mosaic
- knot mosaic

## ASJC Scopus subject areas

- Algebra and Number Theory