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Relations between ( κ , τ ) -regular sets and star complements

Milica Anđelić;  Domingos M. Cardoso;  Slobodan K. Simić — 2013

Czechoslovak Mathematical Journal

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...

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