S.Duzhin. 

Graphes de Moore.

A Moore graph is a regular graph of degree k with k^2+1 vertices.
It is known (*) that Moore graphs can exist only for k=2,3,7,57.
The constructions for k=2,3,7 are well known; the existence of
the "big Moore graph" (for k=57) is still an open problem.
In this paper we give a short proof of theorem (*) and
give a new construction of the Hoffmann-Singleton graph (k=7).