Seminar of Graph Theory - Martin Mačaj (19.4.2018)
Thursday 19.4.2018 at 9:50, Lecture room M/213
By: Martin Škoviera
On a class of self-dual and self-Petrie-dual maps
It is known that the class of regular maps can be identified with the class of groups with a presentation G=<a,b,c: a^2="b^2=c^2=(bc)^2=...1">$. Generally we expect that the group elements 1, a, b, c and bc are pairwise distinct.
In the first part of the talk we give the classification of the maps which fail to meet such expectation, based on the results of C. H. Li and J. Siran.
In the second part of the talk we discuss the construction which gives a self-dual and self-Petrie-dual regular map from any given regular map and study the properties of self-dual and self-Petrie-dual regular maps</a,b,c:>