Springer, Czechoslovak Mathematical Journal, 1(63), p. 73-90, 2013
DOI: 10.1007/s10587-013-0005-5
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Let G be a finite graph with an eigenvalue µ of multiplicity m. A set X of m vertices in G is called a star set for µ in G if µ is not an eigenvalue of the star complement G\X which is the subgraph of G induced by vertices not in X. A vertex subset of a graph is (κ, τ)-regular if it induces a κ-regular subgraph and every vertex not in the subset has τ neighbors in it. We investigate the graphs having a (κ, τ)-regular set which induces a star complement for some eigenvalue. A survey of known results is provided and new properties for these graphs are deduced. Several particular graphs where these properties stand out are presented as examples.