#### 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 ${q}^{n}$-cliques of the graph $\mathsf{Alt}\left(n+1,q\right)$ of $\left(n+1\right)$-dimensional alternating forms over $GF\left(q\right)$, $n\ge 4$, is the unique flag-transitive geometry of rank 3 where planes are isomorphic to the point-line system of $\mathsf{AG}\left(n,q\right)$ 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