Strongly regular Cayley graphs with \(\lambda-\mu=-1\) (Q1331147)

The authors classify the strongly regular graphs \((v,k,\lambda,\mu)\) with \(\lambda-\mu= -1\) which satisfy the additional assumption of being Cayley graphs based on an Abelian group. They prove that, up to complementation, such a graph \(\Gamma\) is either of Payley type, so that its parameters are \((v,(v-1)/2\), \((v-5)/4\), \((v-1)/4)\), or has parameters (243, 22, 1, 2). The proof of this result uses the representation of \(\Gamma\) in terms of a partial difference set. The partial difference sets which are related to the considered graphs have some applications to divisible difference sets which are exploited.