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The signed graphs with two eigenvalues unequal to ±1

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  • Haemers, Willem H.
  • Topcu, Hatice

Abstract

We complete the determination of the signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to ±1. The unsigned graphs and the disconnected, the bipartite and the complete signed graphs with this property have already been determined in two earlier papers. Here we deal with the remaining cases.

Suggested Citation

  • Haemers, Willem H. & Topcu, Hatice, 2024. "The signed graphs with two eigenvalues unequal to ±1," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    • Handle: RePEc:eee:apmaco:v:463:y:2024:i:c:s0096300323005179
    DOI: 10.1016/j.amc.2023.128348
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    References listed on IDEAS

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    1. van Dam, E.R. & Spence, E., 2003. "Combinatorial Designs with Two Singular Values I. Uniform Multiplicative Designs," Discussion Paper 2003-67, Tilburg University, Center for Economic Research.
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    Cited by:

    1. Haemers, Willem H. & Topcu, Hatice, 2023. "Cospectrality Results for Signed Graphs with Two Eigenvalues Unequal to $\pm 1$," Other publications TiSEM a175ce39-b445-4b45-bee1-0, Tilburg University, School of Economics and Management.

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    1. van Dam, E.R. & Haemers, W.H., 2007. "Developments on Spectral Characterizations of Graphs," Discussion Paper 2007-33, Tilburg University, Center for Economic Research.
    2. van Dam, E.R. & Haemers, W.H., 2007. "Developments on Spectral Characterizations of Graphs," Other publications TiSEM 3827c785-7b51-4bcd-aea3-f, Tilburg University, School of Economics and Management.
    3. Haemers, Willem & Topcu, Hatice, 2023. "The Signed Graphs with Two Eigenvalues Unequal to ±1," Other publications TiSEM 7a9accb1-c46e-4c31-a201-e, Tilburg University, School of Economics and Management.
    4. van Dam, E.R. & Spence, E., 2003. "Combinatorial Designs with Two Singular Values II. Partial Geometric Designs," Discussion Paper 2003-94, Tilburg University, Center for Economic Research.
    5. 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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