### 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 |

### Fingerprint

### Keywords

- Cutwidth
- Edge-connectivity
- Finite graph
- Multiplicity

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Tokyo Journal of Mathematics*,

*37*(1), 247-256.

**Multiplicity of finite graphs over the real Line.** / Matsuzaki, Shosaku.

Research output: Contribution to journal › Article

*Tokyo Journal of Mathematics*, vol. 37, no. 1, pp. 247-256.

}

TY - JOUR

T1 - Multiplicity of finite graphs over the real Line

AU - Matsuzaki, Shosaku

PY - 2014/6/1

Y1 - 2014/6/1

N2 - 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 : R1) of a finite graph G over the real line R1 is equal to the cutwidth of G. We give a lower bound of m(G : R1) and determine m(G : R1) for an n-constructed graph G.

AB - 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 : R1) of a finite graph G over the real line R1 is equal to the cutwidth of G. We give a lower bound of m(G : R1) and determine m(G : R1) for an n-constructed graph G.

KW - Cutwidth

KW - Edge-connectivity

KW - Finite graph

KW - Multiplicity

UR - http://www.scopus.com/inward/record.url?scp=84908080553&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84908080553&partnerID=8YFLogxK

M3 - Article

VL - 37

SP - 247

EP - 256

JO - Tokyo Journal of Mathematics

T2 - Tokyo Journal of Mathematics

JF - Tokyo Journal of Mathematics

SN - 0387-3870

IS - 1

ER -