Let G be a graph of order n and let μ be an eigenvalue of multiplicity m. A star complement for μ in G is an induced subgraph of G of order n −m with no eigenvalue μ. In this paper, we study maximal and regular graphs which have Kr,s + tK1 as a star complement for 1 as the second largest eigenvalue. It turns out that some well known strongly regular graphs are uniquely determined by such a star...
