On Adjacency Spectrum of Non-Zero Divisor Graph of \(\mathbb{Z}_n\)
DOI:
https://doi.org/10.26713/cma.v16i1.2938Keywords:
Non-zero divisor graph, Generalized join graph, Adjacency spectrumAbstract
In this article, utilizing the concept of the \(H\)-generalized join graph, we derive the adjacency spectrum of \(\Phi(\mathbb{Z}_{p^k})\), where \(p\) be a prime and \(k \geq 1\) is a positive integer.
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References
D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, Journal of Algebra 217(2) (1999), 434 – 447, DOI: 10.1006/jabr.1998.7840.
I. Beck, Coloring of commutative rings, Journal of Algebra 116(1) (1988), 208 – 226, DOI: 10.1016/0021-8693(88)90202-5.
N. Biggs, Algebraic Graph Theory, Cambridge University Press, England, 205 pages (1974).
D. M. Cardoso, M. A. A. de Freitas, E. A. Martins and M. Robbiano, Spectra of graphs obtained by a generalization of the join graph operation, Discrete Mathematics 313(5) (2013), 733 – 741, DOI: 10.1016/j.disc.2012.10.016.
S. Chattopadhyay, K. L. Patra and B. K. Sahoo, Laplacian eigenvalues of the zerodivisor graph of the ring Zn, Linear Algebra and its Applications 584 (2020), 267 – 286, DOI: 10.1016/j.laa.2019.08.015.
F. Harary, Graph Theory, Addison-Wesley Publishing Company, Reading – Massachusetts, vi + 274 pages (1969).
S. Kadem, A. Aubad and A. H. Majeed, The non-zero divisor graph a ring, Italian Journal of Pure and Applied Mathematics 43 (2020), 975 – 983, URL: https://ijpam.uniud.it/online_issue/202043/82%20AliAubad-SameerKadem-AbdulrahmanMajeed.pdf.
P. M. Magi, S. M. Jose and A. Kishore, Adjacency matrix and eigenvalues of the zero divisor graph Γ(Z)n, Journal of Mathematical and Computational Science 10(4) (2020), 1285 – 1297, URL: https://scik.org/index.php/jmcs/article/view/4590.
P. M. Magi, S. M. Jose and A. Kishore, Spectrum of the zero-divisor graph on the ring of integers modulo n, Journal of Mathematical and Computational Science 10(5) (2020), 1643 – 1666, DOI: 10.28919/jmcs/4719.
S. Pirzada, B. A. Wani and A. Somasundaram, On the eigenvalues of zero-divisor graph associated to finite commutative ring ZpM qN , AKCE International Journal of Graphs and Combinatorics 18(1) (2021), 1 – 6, DOI: 10.1080/09728600.2021.1873060.
M. Young, Adjacency matrices of zero-divisor graphs of integer modulo n, Involve 8(5) (2015), 753 – 761, DOI: 10.2140/involve.2015.8.753.




