Codeterminantal graphs

Aida Abiad; Carlos Alfaro; Kristin Heysse; Marcos Vargas

doi:https://doi.org/10.1016/j.laa.2022.05.021

Codeterminantal graphs

Aida Abiad, Carlos Alfaro, Kristin Heysse, Marcos Vargas

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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.

Original language	English
Pages (from-to)	1-25
Number of pages	25
Journal	Linear Algebra and its Applications
Volume	650
DOIs	https://doi.org/10.1016/j.laa.2022.05.021
Publication status	Published - 1 Oct 2022

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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.",

author = "Aida Abiad and Carlos Alfaro and Kristin Heysse and Marcos Vargas",

year = "2022",

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AU - Abiad, Aida

AU - Alfaro, Carlos

AU - Heysse, Kristin

AU - Vargas, Marcos

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.

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U2 - https://doi.org/10.1016/j.laa.2022.05.021

DO - https://doi.org/10.1016/j.laa.2022.05.021

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VL - 650

SP - 1

EP - 25

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

ER -

Codeterminantal graphs

Abstract

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