On the signless Laplacian and normalized Laplacian spectrum of the zero divisor graphs

Let R be a commutative ring with nonzero identity and let Γ ( R ) denote the zero divisor graph of R . In this paper, we describe the signless Laplacian and normalized Laplacian spectrum of the zero divisor graph Γ ( Z n ) , and we determine these spectrums for some values of n . We also characteriz...

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Bibliographic Details
Published in:Ricerche di matematica 2022-11, Vol.71 (2), p.349-365
Main Authors: Afkhami, Mojgan, Barati, Zahra, Khashyarmanesh, Kazem
Format: Article
Language:English
Subjects:
Algebra
Analysis
Commutativity
Eigenvalues
Geometry
Mathematics
Mathematics and Statistics
Numerical Analysis
Probability Theory and Stochastic Processes
Rings (mathematics)
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Summary:Let R be a commutative ring with nonzero identity and let Γ ( R ) denote the zero divisor graph of R . In this paper, we describe the signless Laplacian and normalized Laplacian spectrum of the zero divisor graph Γ ( Z n ) , and we determine these spectrums for some values of n . We also characterize the cases that 0 is a signless Laplacian eigenvalue of Γ ( Z n ) . Moreover, we find some bounds for some eigenvalues of the signless Laplacian and normalized Laplacian matrices of Γ ( Z n ) .
ISSN:0035-5038
1827-3491
DOI:10.1007/s11587-020-00519-3