On a family of strongly regular graphs with λ=1

In this paper, we give a complete description of strongly regular graphs with parameters ((n2+3n−1)2,n2(n+3),1,n(n+1)). All possible such graphs are: the lattice graph L3,3 with parameters (9,4,1,2), the Brouwer–Haemers graph with parameters (81,20,1,6), and the Games graph with parameters (729,112,1,20).