Signed graphs cospectral with the path

Saieed Akbari; Willem H. Haemers; Hamid Reza Maimani; Leila Parsaei Majd

doi:10.1016/j.laa.2018.04.021

Signed graphs cospectral with the path

Saieed Akbari
, Willem H. Haemers
, Hamid Reza Maimani
, Leila Parsaei Majd

Econometrics and OR

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

16 Citations (Scopus)

Abstract

A signed graph Γ is said to be determined by its spectrum if every signed graph with the same spectrum as Γ is switching isomorphic with Γ. Here it is proved that the path Pn, interpreted as a signed graph, is determined by its spectrum if and only if n≡0,1, or 2 (mod 4), unless n∈{8,13,14,17,29}, or n=3.

Original language	English
Pages (from-to)	104-116
Journal	Linear Algebra and its Applications
Volume	553
DOIs	https://doi.org/10.1016/j.laa.2018.04.021
Publication status	Published - 15 Sept 2018

Keywords

Cospectral graphs
Path
Signed graph
Spectral characterization

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10.1016/j.laa.2018.04.021

http://www.mendeley.com/research/signed-graphs-cospectral-path

Cite this

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title = "Signed graphs cospectral with the path",

abstract = "A signed graph Γ is said to be determined by its spectrum if every signed graph with the same spectrum as Γ is switching isomorphic with Γ. Here it is proved that the path Pn, interpreted as a signed graph, is determined by its spectrum if and only if n≡0,1, or 2 (mod 4), unless n∈\{8,13,14,17,29\}, or n=3.",

keywords = "Cospectral graphs, Path, Signed graph, Spectral characterization",

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AU - Akbari, Saieed

AU - Haemers, Willem H.

AU - Maimani, Hamid Reza

AU - Parsaei Majd, Leila

PY - 2018/9/15

Y1 - 2018/9/15

N2 - A signed graph Γ is said to be determined by its spectrum if every signed graph with the same spectrum as Γ is switching isomorphic with Γ. Here it is proved that the path Pn, interpreted as a signed graph, is determined by its spectrum if and only if n≡0,1, or 2 (mod 4), unless n∈{8,13,14,17,29}, or n=3.

AB - A signed graph Γ is said to be determined by its spectrum if every signed graph with the same spectrum as Γ is switching isomorphic with Γ. Here it is proved that the path Pn, interpreted as a signed graph, is determined by its spectrum if and only if n≡0,1, or 2 (mod 4), unless n∈{8,13,14,17,29}, or n=3.

KW - Cospectral graphs

KW - Path

KW - Signed graph

KW - Spectral characterization

U2 - 10.1016/j.laa.2018.04.021

DO - 10.1016/j.laa.2018.04.021

M3 - Article

SN - 0024-3795

VL - 553

SP - 104

EP - 116

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

Signed graphs cospectral with the path

Abstract

Keywords

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