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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 $\mu$.
In this paper, we study
maximal and regular graphs which have $K_{r,s}+t K_1$ 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
complement.
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