On Normalized Laplacian Spectra of the Weakly Zero-Divisor Graph of the Ring ℤ n

Nazim, Nadeem Ur Rehman and Ahmad Alghamdi ()
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Nazim: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Nadeem Ur Rehman: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Ahmad Alghamdi: Mathematics Department, Faculty of Sciences, Umm Al-Qura University, P.O. Box 14035, Makkah 21955, Saudi Arabia

Mathematics, 2023, vol. 11, issue 20, 1-14

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 .

Keywords: normalized Laplacian spectra; weakly zero-divisor graph; ring of integers modulo n; Euler totient function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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