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On the A α -Eigenvalues of Signed Graphs

Author

Listed:
  • Germain Pastén

    (Departamento de Matemáticas, Universidad Católica del Norte, Antofagasta 1240000, Chile)

  • Oscar Rojo

    (Departamento de Matemáticas, Universidad Católica del Norte, Antofagasta 1240000, Chile)

  • Luis Medina

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile)

Abstract

For α ∈ [ 0 , 1 ] , let A α ( G σ ) = α D ( G ) + ( 1 − α ) A ( G σ ) , where G is a simple undirected graph, D ( G ) is the diagonal matrix of its vertex degrees and A ( G σ ) is the adjacency matrix of the signed graph G σ whose underlying graph is G . In this paper, basic properties of A α ( G σ ) are obtained, its positive semidefiniteness is studied and some bounds on its eigenvalues are derived—in particular, lower and upper bounds on its largest eigenvalue are obtained.

Suggested Citation

  • Germain Pastén & Oscar Rojo & Luis Medina, 2021. "On the A α -Eigenvalues of Signed Graphs," Mathematics, MDPI, vol. 9(16), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1990-:d:618251
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    References listed on IDEAS

    as
    1. Ghorbani, Ebrahim & Haemers, W. H. & Maimani, Hamid Reza & Parsaei Majd, Leila, 2020. "On sign-symmetric signed graphs," Other publications TiSEM 4df47845-b9e6-4bd5-b3db-d, Tilburg University, School of Economics and Management.
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    2. Haemers, Willem H. & Topcu, Hatice, 2021. "On Signed Graphs With at Most Two Eigenvalues Unequal to ±1," Other publications TiSEM 753240bf-5110-4805-af1f-9, Tilburg University, School of Economics and Management.

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