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- Title
On Normalized Laplacian Spectra of the Weakly Zero-Divisor Graph of the Ring ℤ n.
- Authors
Nazim; Rehman, Nadeem Ur; Alghamdi, Ahmad
- Abstract
For a finite commutative ring R with identity 1 ≠ 0 , the weakly zero-divisor graph of R denoted as W Γ (R) is a simple undirected graph having vertex set as a set of non-zero zero-divisors of R and two distinct vertices a and b are adjacent if and only if there exist elements r ∈ ann (a) and s ∈ ann (b) satisfying the condition r s = 0 . The zero-divisor graph of a ring is a spanning sub-graph of the weakly zero-divisor graph. This article finds the normalized Laplacian spectra of the weakly zero-divisor graph W Γ (R) . Specifically, the investigation is carried out on the weakly zero-divisor graph W Γ (Z n) for various values of n.
- Subjects
DIVISOR theory; FINITE rings; COMMUTATIVE rings; UNDIRECTED graphs; RINGS of integers
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 20, p4310
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11204310