Geodesic
Rings associated to finite projective planes and thier isomorphisms
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 9, Tome 289 (2002), pp. 207-213

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In this paper we announce an explicit form of the standard basis of the 2-extended ring associated to the cellular ring generated by the incidence graph of a finite projective plane.This enables us to find the first example of a distance-regular graph satisfying the 6-condition which is not a distance-transivite one. One more corollary of the result obtained is that the cellular rings of any two projective planes of the same order are 2-isomorphic. This implies that if there exist at least two nonisomorphic and nondual to each other projective planes of a given order, then the separability number of any projective plane of this order is greater or equal to 3 and, moreover, it is equal to 3 for a Galois plane. 
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     author = {S. A. Evdokimov and I. N. Ponomarenko},
     title = {Rings associated to finite projective planes and thier isomorphisms},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a10/}
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S. A. Evdokimov; I. N. Ponomarenko. Rings associated to finite projective planes and thier isomorphisms. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 9, Tome 289 (2002), pp. 207-213. http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a10/