On signed graphs with at most two eigenvalues unequal to ±1

Willem H. Haemers; Hatice Topcu

doi:10.1016/j.laa.2023.04.001

On signed graphs with at most two eigenvalues unequal to ±1

Willem H. Haemers^*, Hatice Topcu

^*Corresponding author for this work

Research output: Contribution to journal › Article › Scientific › peer-review

3 Citations (Scopus)

Abstract

We present the first steps towards the determination of the signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to ±1. Here we deal with the disconnected, the bipartite and the complete signed graphs. In addition, we present many examples which cannot be obtained from an unsigned graph or its negative by switching.

Original language	English
Pages (from-to)	68-77
Number of pages	10
Journal	Linear Algebra and its Applications
Volume	670
DOIs	https://doi.org/10.1016/j.laa.2023.04.001
Publication status	Published - 1 Aug 2023

Keywords

Friendship graph
Graph spectrum
Seidel spectrum
Signed graph
Spectral characterization
Symmetric spectrum

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10.1016/j.laa.2023.04.001

Cite this

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title = "On signed graphs with at most two eigenvalues unequal to ±1",

abstract = "We present the first steps towards the determination of the signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to ±1. Here we deal with the disconnected, the bipartite and the complete signed graphs. In addition, we present many examples which cannot be obtained from an unsigned graph or its negative by switching.",

keywords = "Friendship graph, Graph spectrum, Seidel spectrum, Signed graph, Spectral characterization, Symmetric spectrum",

author = "Haemers, {Willem H.} and Hatice Topcu",

note = "Funding Information: We thank Hakan K{\"u}{\c c}{\"u}k for checking which graphs from the list of Stani{\'c} belong to G. Publisher Copyright: {\textcopyright} 2023 The Author(s)",

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AU - Haemers, Willem H.

AU - Topcu, Hatice

PY - 2023/8/1

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N2 - We present the first steps towards the determination of the signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to ±1. Here we deal with the disconnected, the bipartite and the complete signed graphs. In addition, we present many examples which cannot be obtained from an unsigned graph or its negative by switching.

AB - We present the first steps towards the determination of the signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to ±1. Here we deal with the disconnected, the bipartite and the complete signed graphs. In addition, we present many examples which cannot be obtained from an unsigned graph or its negative by switching.

KW - Friendship graph

KW - Graph spectrum

KW - Seidel spectrum

KW - Signed graph

KW - Spectral characterization

KW - Symmetric spectrum

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M3 - Article

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VL - 670

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JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

On signed graphs with at most two eigenvalues unequal to ±1

Abstract

Keywords

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