Speaker
Prof.
Gábor Gévay
(University of Szeged)
Description
We state the following theorem: a generalized Petersen graph is the 1-skeleton of a regular map if and only if it belongs to the following set:
{GP(4,1),GP(5,2),GP(8,3),GP(10,2),GP(10,3),GP(12,5),GP(24,5)}. These graphs are precisely those which are known to be the only arc-transitive generalized Petersen graphs; hence we only have to prove the ``if" part of our theorem. Five of the corresponding regular maps are well known. Little is known, however, about the regular maps associated with GP(10,3) and GP(24,5). This is especially surprising in the case of GP(10,3), which is the well-known Desargues graph, i.e. the Levi graph of the Desargues configuration. We outline the proof of regularity of these latter maps and briefly discuss some of their properties.
Primary author
Prof.
Gábor Gévay
(University of Szeged)
