On Normalized Laplacian Spectra of the Weakly Zero-Divisor Graph of the Ring ℤn - Nazim; Nadeem Ur Rehman; Ahmad Alghamdi (Mathematics, 2023)
For a finite commutative ring <semantics>R</semantics> with identity <semantics>1≠0</semantics>, the weakly zero-divisor graph of <semantics>R</semantics> denoted as <semantics>WΓ(R)</semantics> is a simple undirected graph having vertex set as a set of non-zero zero-divisors of <semantics>R</semantics> and two distinct vertices <semantics>a</semantics> and <semantics>b</semantics> are adjacent if and only if there exist elements <semantics>r∈ann(a)</semantics> and <semantics>s∈ann(b)</semantics> satisfying the condition <semantics>rs=0</semantics>. 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 <semantics>WΓ(R)</semantics>. Specifically, the investigation is carried out on the weakly zero-divisor graph <semantics>WΓ(Zn)</semantics> for various values of <semantics>n</semantics>.