Codeterminantal graphs

Aida Abiad; Carlos A. Alfaro; Kristin Heysse; Marcos C. Vargas

doi:10.1016/j.laa.2022.05.021

Codeterminantal graphs

Aida Abiad, Carlos A. Alfaro, Kristin Heysse, Marcos C. Vargas

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

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We introduce the concept of codeterminantal graphs, which generalize the concepts of cospectral and coinvariant graphs. To do this, we investigate the relationship of the spectrum and the Smith normal form (SNF) with the determinantal ideals. We establish a necessary and sufficient condition for graphs to be codeterminantal on R[x], and we present some computational results on codeterminantal graphs up to 9 vertices. Finally, we show that complete graphs and star graphs are determined by the SNF of its distance Laplacian matrix.

Originele taal-2	Engels
Pagina's (van-tot)	1-25
Aantal pagina's	25
Tijdschrift	Linear Algebra and Its Applications
Volume	650
DOI's	https://doi.org/10.1016/j.laa.2022.05.021
Status	Gepubliceerd - 1 okt. 2022

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© 2022 Elsevier Inc.

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title = "Codeterminantal graphs",

abstract = "We introduce the concept of codeterminantal graphs, which generalize the concepts of cospectral and coinvariant graphs. To do this, we investigate the relationship of the spectrum and the Smith normal form (SNF) with the determinantal ideals. We establish a necessary and sufficient condition for graphs to be codeterminantal on R[x], and we present some computational results on codeterminantal graphs up to 9 vertices. Finally, we show that complete graphs and star graphs are determined by the SNF of its distance Laplacian matrix.",

keywords = "Cospectral graph, Determinantal ideal, Distance Laplacian matrix, Graph spectrum, Sandpile group, Smith normal form",

author = "Aida Abiad and Alfaro, \{Carlos A.\} and Kristin Heysse and Vargas, \{Marcos C.\}",

note = "Funding Information: Carlos A. Alfaro and Marcos C. Vargas are partially supported by CONACYT and SNI . Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

year = "2022",

month = oct,

day = "1",

doi = "10.1016/j.laa.2022.05.021",

language = "English",

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TY - JOUR

T1 - Codeterminantal graphs

AU - Abiad, Aida

AU - Alfaro, Carlos A.

AU - Heysse, Kristin

AU - Vargas, Marcos C.

PY - 2022/10/1

Y1 - 2022/10/1

N2 - We introduce the concept of codeterminantal graphs, which generalize the concepts of cospectral and coinvariant graphs. To do this, we investigate the relationship of the spectrum and the Smith normal form (SNF) with the determinantal ideals. We establish a necessary and sufficient condition for graphs to be codeterminantal on R[x], and we present some computational results on codeterminantal graphs up to 9 vertices. Finally, we show that complete graphs and star graphs are determined by the SNF of its distance Laplacian matrix.

AB - We introduce the concept of codeterminantal graphs, which generalize the concepts of cospectral and coinvariant graphs. To do this, we investigate the relationship of the spectrum and the Smith normal form (SNF) with the determinantal ideals. We establish a necessary and sufficient condition for graphs to be codeterminantal on R[x], and we present some computational results on codeterminantal graphs up to 9 vertices. Finally, we show that complete graphs and star graphs are determined by the SNF of its distance Laplacian matrix.

KW - Cospectral graph

KW - Determinantal ideal

KW - Distance Laplacian matrix

KW - Graph spectrum

KW - Sandpile group

KW - Smith normal form

UR - http://www.scopus.com/inward/record.url?scp=85132450638&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2022.05.021

DO - 10.1016/j.laa.2022.05.021

M3 - Article

AN - SCOPUS:85132450638

SN - 0024-3795

VL - 650

SP - 1

EP - 25

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Codeterminantal graphs

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