Abstract
An outindependent subgraph of a graph Γ, with respect to an independent vertex subset C⊂ V, is the subgraph ΓC induced by the vertices in V∖ C. We study the case when Γ is strongly regular, where the results of de Caen [1998, The spectra of complementary subgraphs in a strongly regular graph. European Journal of Combinatorics, 19(5), 559–565.], allow us to derive the whole spectrum of ΓC . Moreover, when C attains the Hoffman–Lovász bound for the independence number, ΓC is a regular graph (in fact, distance-regular if Γ is a Moore graph). This article is mainly devoted to study the non-regular case. As a main result, we characterize the structure of ΓC when C is the neighborhood of either one vertex or one edge.
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