On the characterization of graphs by star complements

Let G be a graph of order n and μ be an adjacency eigenvalue of G with multiplicity k≥1. A star complement for μ in G is an induced subgraph of G of order n−k with no eigenvalue μ. In this paper, all the regular graphs with K1,1,t as a star complement are determined. Also, the maximal graphs with K1,1,t(t≠8,9) as a star complement for the eigenvalue μ=1, and K7 as a star complement for the eigenvalue μ=−2 are described.