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Let  Γ  be a diameter 3 distance-regular graph with a strongly regular graph  Γ  3 , where  Γ  3  is the graph whose vertex set coincides with the vertex set of the graph  Γ  and two vertices are adjacent whenever they are at distance 3 in the graph  Γ . Computing the parameters of  Γ  3  by the intersection array of the graph  Γ  is considered as the direct problem. Recovering the intersection array of the graph  Γ  by the parameters of  Γ  3  is referred to as the inverse problem. The inverse problem for  Γ  3  has been solved earlier by A. A. Makhnev and M. S. Nirova. In the case where  Γ  3  is a pseudo-geometric graph of a net, a series of admissible intersection arrays has been obtained: { c  2 ( u  2  −  m  2 ) + 2 c  2  m  −  c  2  − 1,  c  2 ( u  2  −  m  2 ), ( c  2  − 1)( u  2  −  m  2 ) + 2 c  2  m  −  c  2 ; 1,  c  2 ,  u  2  −  m  2 } (A. A. Makhnev, Wenbin Guo, M. P. Golubyatnikov). The cases  c  2  = 1 and  c  2  = 2 have been examined by A. A. Makhnev, M. P. Golubyatnikov and A. A. Makhnev, M. S. Nirova, respectively.

On small distance-regular graphs with the intersection arrays { mn − 1, ( m − 1)( n + 1), n − m + 1; 1, 1, ( m − 1)( n + 1)}