On Regular Graphs with Complete Tripartite Star Complements

Let G be a graph of order n and let mu be an eigenvalue of multiplicity m. A star complement for mu in G is an induced subgraph of G of order n in with no eigenvalue A. Some general observations concerning graphs with the complete tripartite graph K-r,K-s,K-t as a star complement. We study the maximal regular graphs which have K-n,K-n,K-n as a star complement for eigenvalue mu. The results include a complete analysis of the regular graphs which have Kn,n,n as a star complement for 1. It turns out that some well known strongly regular graphs are uniquely determined by such a star complement.