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 \(n-m\) with no eigenvalue \(\mu\). Some general observations concerning graphs with the complete tripartite graph \(K_{r,s,t}\) as a star complement are made. We study the maximal regular graphs which have \(K_{r,s,t}\) as a star complement for eigenvalue \(\mu\). The results include a complete analysis of the regular graphs which have \(K_{n,n,n}\) as a star complement for \(\mu = 1\). It turns out that some well-known strongly regular graphs are uniquely determined by such a star complement.
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