Four Constructions of Highly Symmetric Tetravalent Graphs
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 -transitive are considered.
graph graph dart cubic graph capping symmetry map corners