Abstract
We give an arithmetical characterization of graphs which are realizable as graphs of the lattice ℒ of the subspaces of a graphic (or projective) space of finite dimension and of finite order q ≥ 1. In other words ℒ is any complemented modular lattice of finite rank and of finite order q. When q ≥ 2 and the rank is at least four, ℒ is the lattice of the subspaces of a finite dimensional vector space over the field GF(q). Two independent axioms are required involving the number of geodesies between any two vertices. This number must be a simple function of the distance.
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