Classification of some strongly regular subgraphs of the McLaughlin graph

AbstractBy 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