SEIDEL SPECTRUM OF THE ZERO-DIVISOR GRAPH ON THE RING OF INTEGERS MODULO n

Magi, P. M.; Jose, Sr. Magie; Kishore, Anjaly

doi:10.17654/dm028010145

Cited by 3 publications

(2 citation statements)

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“…Also, the normalized Laplacian spectra of power graphs associated with finite cyclic groups were discussed in [12]. Different spectra of zero-divisor graphs have been examined in prior works [13][14][15]. Also, some works on a space-time spectral order, a predictor-corrector compact difference, an implicit robust numerical scheme and an efficient ADI difference scheme are found in [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

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

Nazim,

Rehman,

Alghamdi

2023

Mathematics

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For a finite commutative ring R with identity 1≠0, the weakly zero-divisor graph of R denoted as WΓ(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 rs=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 WΓ(R). Specifically, the investigation is carried out on the weakly zero-divisor graph WΓ(Zn) for various values of n.

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Section: Introductionmentioning

confidence: 99%

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

Nazim,

Rehman,

Alghamdi

2023

Mathematics

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“…In [9], they showed that the zero divisor graph of ring Z p l is Laplacian integral for every prime p and l ≥ 2 is a positive integer. The work on adjacency spectrum, signless spectrum, distance signless spectrum of zero-divisor graph can be found in [10,13,14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

On the cozero-divisor graphs assosciated to rings

Praveen¹,

Kumar²

2022

Preprint

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Let R be a ring with unity. The cozero-divisor graph of a ring R, denoted by Γ (R), is an undirected simple graph whose vertices are the set of all non-zero and non-unit elements of R, and two distinct vertices x and y are adjacent if and only if x / ∈ Ry and y / ∈ Rx. In this paper, we study the Laplacian spectrum of Γ (Zn). We show that the graph Γ (Zpq) is Laplacian integral. Further, we obtain the Laplacian spectrum Γ (Zn) for n = p n 1 q n 2 ,where n 1 , n 2 ∈ N and p, q are distinct primes.

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Aγ Eigenvalues of Zero Divisor Graph of Integer Modulo and Von Neumann Regular Rings

Rather

Ali

Ullah³

et al. 2022

Symmetry

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The Aγ matrix of a graph G is determined by Aγ(G)=(1−γ)A(G)+γD(G), where 0≤γ≤1, A(G) and D(G) are the adjacency and the diagonal matrices of node degrees, respectively. In this case, the Aγ matrix brings together the spectral theories of the adjacency, the Laplacian, and the signless Laplacian matrices, and many more γ adjacency-type matrices. In this paper, we obtain the Aγ eigenvalues of zero divisor graphs of the integer modulo rings and the von Neumann rings. These results generalize the earlier published spectral theories of the adjacency, the Laplacian and the signless Laplacian matrices of zero divisor graphs.

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SEIDEL SPECTRUM OF THE ZERO-DIVISOR GRAPH ON THE RING OF INTEGERS MODULO n

Cited by 3 publications

References 0 publications

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

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

On the cozero-divisor graphs assosciated to rings

Aγ Eigenvalues of Zero Divisor Graph of Integer Modulo and Von Neumann Regular Rings

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