Abstract
Let R be a commutative ring with nonzero identity and let \(\Gamma (R)\) denote the zero divisor graph of R. In this paper, we describe the signless Laplacian and normalized Laplacian spectrum of the zero divisor graph \(\Gamma (\mathbb {Z}_n)\), and we determine these spectrums for some values of n. We also characterize the cases that 0 is a signless Laplacian eigenvalue of \(\Gamma (\mathbb {Z}_n)\). Moreover, we find some bounds for some eigenvalues of the signless Laplacian and normalized Laplacian matrices of \(\Gamma (\mathbb {Z}_n)\).
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Afkhami, M., Barati, Z. & Khashyarmanesh, K. On the signless Laplacian and normalized Laplacian spectrum of the zero divisor graphs. Ricerche mat 71, 349–365 (2022). https://doi.org/10.1007/s11587-020-00519-3
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DOI: https://doi.org/10.1007/s11587-020-00519-3
Keywords
- Zero divisor graph
- Signless Laplacian spectrum
- Normalized Laplacian spectrum
- Smallest signless Laplacian eigenvalue
- Largest signless Laplacian eigenvalue