### Abstract

For topological spaces X and Y, the multiplicity m(X : Y) of X over Y is defined by M. Gromov and K. Taniyama independently. We show that the multiplicity m(G : R^{1}) of a finite graph G over the real line R^{1} is equal to the cutwidth of G. We give a lower bound of m(G : R^{1}) and determine m(G : R^{1}) for an n-constructed graph G.

Original language | English |
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Pages (from-to) | 247-256 |

Number of pages | 10 |

Journal | Tokyo Journal of Mathematics |

Volume | 37 |

Issue number | 1 |

Publication status | Published - 2014 Jun 1 |

### Keywords

- Cutwidth
- Edge-connectivity
- Finite graph
- Multiplicity

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Matsuzaki, S. (2014). Multiplicity of finite graphs over the real Line.

*Tokyo Journal of Mathematics*,*37*(1), 247-256.