### Spectrum of the zero-divisor graph on the ring of integers modulo n

#### Abstract

For a commutative ring R with non-zero identity, let Z∗(R) denote the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by Γ(R), is a simple undirected graph with all non-zero zero-divisors as vertices and two distinct vertices x, y ∈ Z∗(R) are adjacent if and only if xy = 0. In this paper, the adjacency matrix and spectrum of Γ(Zpk ) are investigated. Also, the implicit computation of the spectrum of Γ(Zn) is described.

**Published:**2020-06-29

**How to Cite this Article:**P.M. Magi, Sr. Magie Jose, Anjaly Kishore, Spectrum of the zero-divisor graph on the ring of integers modulo n, J. Math. Comput. Sci., 10 (2020), 1643-1666 Copyright © 2020 P.M. Magi, Sr. Magie Jose, Anjaly Kishore. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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