Authors: Biyikoglu, Turker
Simić, Slobodan 
Stanić, Zoran
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Some notes on spectra of cographs
Journal: Ars Combinatoria
Volume: 100
First page: 421
Last page: 434
Issue Date: 1-Jul-2011
Rank: M23
ISSN: 0381-7032
A cograph is a P4-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 √5-1/2 is unique.
Keywords: σ-graph | Characteristic polynomial | Cograph | Eigenvalues | Polynomial reconstruction
Publisher: Charles Babbage Research Centre

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