Adjacency spectrum and energy of the exact zero-divisor graph of $\mathbb{Z}_n$
نویسندگان
1 Department of Mathematics, Dr. Subhash University, P.O. Box 362001, Junagadh, India.
2 Department of Mathematics, Dr. Subhash University, P.O. Box 362001, Junagadh, India.
doi
10.30504/jims.2025.546348.1284چکیده
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.
