### Adjacency matrix and eigenvalues of the zero divisor graph Γ(Zn)

#### Abstract

Let R be a commutative ring with non-zero identity and Z^∗(R) be 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 eigenvalues of Γ(Zn) for n = p^2q^2, where p and q are distinct primes, are investigated. Also, the girth, diameter, clique number and stability number of this graph are found.

**Published:**2020-05-12

**How to Cite this Article:**P.M. Magi, Sr. Magie Jose, Anjaly Kishore, Adjacency matrix and eigenvalues of the zero divisor graph Γ(Zn), J. Math. Comput. Sci., 10 (2020), 1285-1297 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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