19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
Home > Timetable > Contribution details

Neighbour-transitive incidence structures in odd graphs, a few examples.

Presented by Dr. Eugenia O'REILLY-REGUEIRO
Type: Oral presentation
Track: Polytopes and Incidence Geometries


For k>0 and a set X of size 2k+1, the odd graph O_{k+1} is a (k+1)-regular graph whose vertices are the k-sets of X and in which two vertices are adjacent if and only if they are disjoint. For a subset $\Gamma$ of V(O_{k+1}), the incidence relation between the elements of X and the elements of $\Gamma$ yields an incidence structure. We define $\Gamma_1$ as the set of neighbours of $\Gamma$ in this incidence structure thus: $\Gamma_1$ is the set of vertices of O_{k+1} that are not in $\Gamma$ and are adjacent in the graph to at least one element of $\Gamma$. We place no restrictions on the choice of $\Gamma$ but ask the automorphism group of this incidence structure to be transitive on $\Gamma_1$. In this talk we present some examples of these incidence structures.


Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

Primary authors