32 research outputs found
Truncation symmetry type graphs
There are operations that transform a map M (an embedding of a graph on a
surface) into another map in the same surface, modifying its structure and
consequently its set of flags F(M). For instance, by truncating all the
vertices of a map M, each flag in F(M) is divided into three flags of the
truncated map. Orbanic, Pellicer and Weiss studied the truncation of k-orbit
maps for k < 4. They introduced the notion of T-compatible maps in order to
give a necessary condition for a truncation of a k-orbit map to be either k-,
3k/2- or 3k-orbit map. Using a similar notion, by introducing an appropriate
partition on the set of flags of the maps, we extend the results on truncation
of k-orbit maps for k < 8 and k=9
Medial symmetry type graphs
A -orbit map is a map with its automorphism group partitioning the set of
flags into orbits. Recently -orbit maps were studied by Orbani\' c,
Pellicer and Weiss, for . In this paper we use symmetry type graphs
to extend such study and classify all the types of -orbit maps, as well as
all self-dual, properly and improperly, symmetry type of -orbit maps with
. Moreover, we determine, for small values of , all types of
-orbits maps that are medial maps. Self-dualities constitute an important
tool in this quest