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Abstract  A Deza graph with parameters    (   v  ,  k  ,  b  ,  a   )    is a   k  ‐regular graph on   v   vertices in which the number of common neighbors of two distinct vertices takes one of the following values:   b   or   a  , where   b  ≥  a  . In the previous papers Deza graphs with   b  =  k  −  1   were characterized. In this paper, we characterize Deza graphs with   b  =  k  −  2  .

Deza graphs with parameters ( v , k , k − 2 , a )