A characterization of the geometry of large maximal cliques of the alternating forms graph

We prove that the geometry of vertices, edges and $q^{n}$ -cliques of the graph $Alt (n + 1, q)$ of $(n + 1)$ -dimensional alternating forms over $GF (q)$ , $n \geq 4$ , is the unique flag-transitive geometry of rank 3 where planes are isomorphic to the point-line system of $AG (n, q)$ and the star of a point is dually isomorphic to a projective space.

Keywords

diagram geometry, linear-dual-linear geometries, distance regular graphs, alternating forms graphs

Mathematical Subject Classification 2000

Primary: 05E20, 05E30, 51E24

Milestones

Received: 15 August 2007

Accepted: 28 October 2007

Authors

Antonio Pasini
Department of Information Engineering and Mathematics University of Siena Via Roma 56 53100 Siena Italy

Vol. 8, No. 1, 2008

Antonio Pasini

Abstract

Keywords

Mathematical Subject Classification 2000

Milestones

Authors