Four constructions of highly symmetric tetravalent graphs

Aaron Hill, Steve Wilson

Research output: Contribution to journalArticle

3 Scopus citations

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 languageEnglish (US)
Pages (from-to)229-244
Number of pages16
JournalJournal of Graph Theory
Volume71
Issue number3
DOIs
StatePublished - Nov 2012

Keywords

  • Capping
  • Corners
  • Cubic Graph
  • Dart
  • Graph
  • Map
  • Symmetry

ASJC Scopus subject areas

  • Geometry and Topology

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