Journal of the Iranian Mathematical Society

Journal of the Iranian Mathematical Society

Adjacency ‎s‎pectrum and energy of the exact zero-divisor graph of $\mathbb{Z}_n‏$

Document Type : Research Article

Authors
S. K. Babariya
P. T. Lalchandani
Department of‎ ‎Mathematics, Dr‎. ‎Subhash University‎, ‎P.O‎. ‎Box 362001, Junagadh‎, ‎India.
10.30504/jims.2025.546348.1284
Abstract
This paper investigates the exact zero-divisor graph $E\Gamma(R)$ of a commutative ring‎, ‎with particular focus on $R=\mathbb{Z}_n$‎. ‎We describe a partition of the vertex set of $E\Gamma(\mathbb{Z}_n)$ based on the greatest common divisors with $n$‎, ‎which provides structural information about its components‎. ‎The adjacency spectra and energies of $E\Gamma(\mathbb{Z}_{p^{2m+1}})$ and $E\Gamma(\mathbb{Z}_{p^{2m}})$ are computed explicitly‎, ‎and their asymptotic behaviors are compared‎. ‎The results reveal clear structural differences between the odd and even power cases‎.
Keywords
&lrm
Exact zero-divisor graph&lrm
adjacency matrix&lrm
, &lrm
generalized join graph
Subjects
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Journal of the Iranian Mathematical Society
Volume 6, Issue 2
August 2025
Pages 149-158