Algebraic Graph Theory - Hendrik Van Maldeghem

Monday, July 24, 2023 11:30 am - 11:30 am EDT (GMT -04:00)

Title: Geometric approach to some rank 3 graphs

Speaker: Hendrik Van Maldeghem
Affiliation: Ghent University
Location: Please contact Sabrina Lato for Zoom link

Abstract: Rank 3 graphs are graphs whose full automorphism group acts as a rank 3 group on the vertices. Finite rank 3 groups are classified and hence finite rank 3 graphs are classified. The main examples arise from geometric structures such as projective and polar spaces, and there is one class of examples related to the exceptional groups of type E6. We present a combinatorial/geometric/projective construction of these graphs.  We then consider a class of regular sets, that is, subsets S of the vertices such that the number of vertices of S adjacent to some vertex v only depends on whether v belongs to S or not. We will explain how this leads to characterizations of certain automorphisms of the E6 graphs and other graphs.