### Abstract

We show that two embeddings f and g of a finite graph G into the 3-space are spatial-graph-homologous if and only if for each subgraph H of G that is homeomorphic to a disjoint union of two circles, the restriction maps f _{H} and g _{H} have the same linking number, and for each subgraph H of G that is homeomorphic to a complete graph K_{5} or a complete bipartite graph K_{3,3}, the restriction maps f _{H} and g _{H} have the same Simon invariant.

Original language | English |
---|---|

Pages (from-to) | 53-67 |

Number of pages | 15 |

Journal | Topology and its Applications |

Volume | 134 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2003 Oct 15 |

### Fingerprint

### Keywords

- Delta move
- Finite type invariant
- Linking number
- Simon invariant
- Spatial graph
- Spatial-graph-homology

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

**Homology classification of spatial graphs by linking numbers and Simon invariants.** / Shinjo, Reiko; Taniyama, Kouki.

Research output: Contribution to journal › Article

*Topology and its Applications*, vol. 134, no. 1, pp. 53-67. https://doi.org/10.1016/S0166-8641(03)00101-9

}

TY - JOUR

T1 - Homology classification of spatial graphs by linking numbers and Simon invariants

AU - Shinjo, Reiko

AU - Taniyama, Kouki

PY - 2003/10/15

Y1 - 2003/10/15

N2 - We show that two embeddings f and g of a finite graph G into the 3-space are spatial-graph-homologous if and only if for each subgraph H of G that is homeomorphic to a disjoint union of two circles, the restriction maps f H and g H have the same linking number, and for each subgraph H of G that is homeomorphic to a complete graph K5 or a complete bipartite graph K3,3, the restriction maps f H and g H have the same Simon invariant.

AB - We show that two embeddings f and g of a finite graph G into the 3-space are spatial-graph-homologous if and only if for each subgraph H of G that is homeomorphic to a disjoint union of two circles, the restriction maps f H and g H have the same linking number, and for each subgraph H of G that is homeomorphic to a complete graph K5 or a complete bipartite graph K3,3, the restriction maps f H and g H have the same Simon invariant.

KW - Delta move

KW - Finite type invariant

KW - Linking number

KW - Simon invariant

KW - Spatial graph

KW - Spatial-graph-homology

UR - http://www.scopus.com/inward/record.url?scp=0042381265&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042381265&partnerID=8YFLogxK

U2 - 10.1016/S0166-8641(03)00101-9

DO - 10.1016/S0166-8641(03)00101-9

M3 - Article

AN - SCOPUS:0042381265

VL - 134

SP - 53

EP - 67

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 1

ER -