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 |
Keywords
- Capping
- Corners
- Cubic Graph
- Dart
- Graph
- Map
- Symmetry
ASJC Scopus subject areas
- Geometry and Topology