### Abstract

Given a connected, dart-transitive, cubic graph, constructions of its Hexagonal Capping and its Dart Graph are considered. In each case, the result is a tetravalent graph which inherits symmetry from the original graph and is a covering of the line graph.Similar constructions are then applied to a map (a cellular embedding of a graph in a surface) giving tetravalent coverings of the medial graph. For each construction, conditions on the graph or the map to make the constructed graph dart-transitive, semisymmetric or 1/2-transitive are considered.

Original language | English (US) |
---|---|

Pages (from-to) | 229-244 |

Number of pages | 16 |

Journal | Journal of Graph Theory |

Volume | 71 |

Issue number | 3 |

DOIs | |

State | Published - Nov 2012 |

### Fingerprint

### Keywords

- Capping
- Corners
- Cubic Graph
- Dart
- Graph
- Map
- Symmetry

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Journal of Graph Theory*,

*71*(3), 229-244. https://doi.org/10.1002/jgt.20520

**Four constructions of highly symmetric tetravalent graphs.** / Hill, Aaron; Wilson, Steve.

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 71, no. 3, pp. 229-244. https://doi.org/10.1002/jgt.20520

}

TY - JOUR

T1 - Four constructions of highly symmetric tetravalent graphs

AU - Hill, Aaron

AU - Wilson, Steve

PY - 2012/11

Y1 - 2012/11

N2 - Given a connected, dart-transitive, cubic graph, constructions of its Hexagonal Capping and its Dart Graph are considered. In each case, the result is a tetravalent graph which inherits symmetry from the original graph and is a covering of the line graph.Similar constructions are then applied to a map (a cellular embedding of a graph in a surface) giving tetravalent coverings of the medial graph. For each construction, conditions on the graph or the map to make the constructed graph dart-transitive, semisymmetric or 1/2-transitive are considered.

AB - Given a connected, dart-transitive, cubic graph, constructions of its Hexagonal Capping and its Dart Graph are considered. In each case, the result is a tetravalent graph which inherits symmetry from the original graph and is a covering of the line graph.Similar constructions are then applied to a map (a cellular embedding of a graph in a surface) giving tetravalent coverings of the medial graph. For each construction, conditions on the graph or the map to make the constructed graph dart-transitive, semisymmetric or 1/2-transitive are considered.

KW - Capping

KW - Corners

KW - Cubic Graph

KW - Dart

KW - Graph

KW - Map

KW - Symmetry

UR - http://www.scopus.com/inward/record.url?scp=84865791034&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865791034&partnerID=8YFLogxK

U2 - 10.1002/jgt.20520

DO - 10.1002/jgt.20520

M3 - Article

VL - 71

SP - 229

EP - 244

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 3

ER -