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Discussiones Mathematicae Graph Theory
Article . 2024 . Peer-reviewed
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Spectral bounds for the zero forcing number of a graph

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2024 English Publisher:University of Zielona Góra, PolandJournal:Discussiones Mathematicae Graph Theory, volume 44, page 971 (issn: 1234-3099, eissn: 2083-5892, Copyright policy )
Authors: Hongzhang Chen; Jianxi Li; Shou-Jun Xu;

doi: 10.7151/dmgt.2482

Spectral bounds for the zero forcing number of a graph

Abstract

Summary: Let \(Z(G)\) be the zero forcing number of a simple connected graph \(G\). In this paper, we study the relationship between the zero forcing number of a graph and its (normalized) Laplacian eigenvalues. We provide the upper and lower bounds on \(Z(G)\) in terms of its (normalized) Laplacian eigenvalues, respectively. Our bounds extend the existing bounds for regular graphs.

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Keywords

Connectivity, Eigenvalues, singular values, and eigenvectors, bound, Graphs and linear algebra (matrices, eigenvalues, etc.), QA1-939, eigenvalue, zero forcing number, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Top 10%
Average
Average
Published in a Diamond OA journal