Authors: Bell, Francis
Simić, Slobodan 
Title: On graphs whose star complement for -2 is a path or a cycle
Journal: Linear Algebra and Its Applications
Volume: 377
Issue: 1-3
First page: 249
Last page: 265
Issue Date: 15-Jan-2004
Rank: M22
ISSN: 0024-3795
DOI: 10.1016/j.laa.2003.08.016
It was proved recently by one of the authors that, if H is a path P t (t > 2 with t ≠ 7 or 8) or an odd cycle Ct (t > 3), then there is a unique maximal graph having H as a star complement for -2. The methods employed were analytical in nature, making use of the Reconstruction Theorem for star complements. Here we offer an alternative approach, based on the forbidden subgraph technique. In addition, we resolve the exceptional situations arising when H = P7 or P8.
Keywords: Adjacency matrix | Cycle | Exceptional graph | Graph eigenvalues | Path
Publisher: Elsevier

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