Vol. 8, No. 1, 2008

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

Antonio Pasini

Vol. 8 (2008), No. 1, 81–116
Abstract

We prove that the geometry of vertices, edges and qn-cliques of the graph Alt(n + 1,q) of (n + 1)-dimensional alternating forms over GF(q), n 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