A complete characterization of graphs with exactly two positive eigenvalues

A complete characterization of graphs with exactly two positive eigenvalues

In 1977, Smith has characterized graphs with exactly one positive eigenvalue. Since then, many particular results related to graphs with exactly two positive eigenvalues have emerged. In this paper we conclude this investigation by giving a full characterization of these graphs.

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Veröffentlicht in:Advances in applied mathematics 2023-03, Vol.144, p.102457, Article 102457
Hauptverfasser: Duan, Fang, Huang, Qiongxiang, Huang, Xueyi, Stanić, Zoran, Wang, Jianfeng
Format: Artikel
Sprache:eng
Schlagworte:
Congruent vertex
Forbidden subgraph
Nullity
Positive (negative) inertia index
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Zusammenfassung:In 1977, Smith has characterized graphs with exactly one positive eigenvalue. Since then, many particular results related to graphs with exactly two positive eigenvalues have emerged. In this paper we conclude this investigation by giving a full characterization of these graphs.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2022.102457