Abstract
By means of an exhaustive computer search we have proved that the strongly regular graphs with parameters ( v , k , λ , μ ) = ( 105 , 32 , 4 , 12 ) , ( 120 , 42 , 8 , 18 ) and ( 176 , 70 , 18 , 34 ) are unique up to isomorphism. Each of these graphs occurs as an induced subgraph in the strongly regular McLaughlin graph. We have used an orderly backtracking algorithm with look-ahead and look-back strategies, applying constraints based on several combinatorial and algebraic properties of graphs with the given parameters.
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