|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||Abstract:||
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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