Some notes on spectra of cographs
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CitationBıyıkoğlu, T., Simic, S. K. & Stanic, Z. (2011). Some notes on spectra of cographs. Ars Combinatoria, 100, 421-434.
A cograph is a P-4-free graph. We first give a short proof of the fact that 0 (-1) belongs to the spectrum of a connected cograph (with at least two vertices) if and only if it contains duplicate (resp. coduplicate) vertices. As a consequence, we next prove that the polynomial reconstruction of graphs whose vertex-deleted subgraphs have the second largest eigenvalue not exceeding root 5-1/2 is unique.