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

2021 ◽  
Vol 28 (1) ◽  
pp. 145-167
Author(s):  
P. M. Magi ◽  
Sr. Magie Jose ◽  
Anjaly Kishore
Keyword(s):  
Zero Divisor ◽  
Ring Of Integers ◽  
Zero Divisor Graph

scholarly journals On Laplacian Eigenvalues of the Zero-Divisor Graph Associated to the Ring of Integers Modulo n

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 482
Author(s):  
Bilal A. Rather ◽  
Shariefuddin Pirzada ◽  
Tariq A. Naikoo ◽  
Yilun Shang
Keyword(s):  
Commutative Ring ◽  
Zero Divisor ◽  
Simple Graph ◽  
Laplacian Spectrum ◽  
Laplacian Eigenvalues ◽  
Ring Of Integers ◽  
Zero Divisor Graph ◽  
Zero Divisors ◽  
Vertex Set ◽  
Positive Integers

Given a commutative ring R with identity 1≠0, let the set Z(R) denote the set of zero-divisors and let Z*(R)=Z(R)∖{0} be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by Γ(R), is a simple graph whose vertex set is Z*(R) and each pair of vertices in Z*(R) are adjacent when their product is 0. In this article, we find the structure and Laplacian spectrum of the zero-divisor graphs Γ(Zn) for n=pN1qN2, where p<q are primes and N1,N2 are positive integers.

Automorphisms of the zero-divisor graph of 2 × 2 matrix ring over ℤps

2017 ◽  
Vol 16 (12) ◽  
pp. 1750227 ◽  
Author(s):  
Hengbin Zhang ◽  
Jizhu Nan ◽  
Gaohua Tang
Keyword(s):  
Positive Integer ◽  
Directed Graph ◽  
Zero Divisor ◽  
Matrix Ring ◽  
Directed Edge ◽  
Ring Of Integers ◽  
Zero Divisor Graph ◽  
Zero Divisors

Let [Formula: see text] be the ring of integers modulo [Formula: see text] where [Formula: see text] is a prime and [Formula: see text] is a positive integer, [Formula: see text] the [Formula: see text] matrix ring over [Formula: see text]. The zero-divisor graph of [Formula: see text], written as [Formula: see text], is a directed graph whose vertices are nonzero zero-divisors of [Formula: see text], and there is a directed edge from a vertex [Formula: see text] to a vertex [Formula: see text] if and only if [Formula: see text]. In this paper, we completely determine the automorphisms of [Formula: see text].

scholarly journals The non-zero divisor graph of ring of integers modulo six and the Hamiltonian quaternion over integers modulo two

2021 ◽  
Vol 1988 (1) ◽  
pp. 012074
Author(s):  
Nur Athirah Farhana Omar Zai ◽  
Nor Haniza Sarmin ◽  
Sanhan Muhammad Salih Khasraw ◽  
Ibrahim Gambo ◽  
Nurhidayah Zaid
Keyword(s):  
Zero Divisor ◽  
Ring Of Integers ◽  
Zero Divisor Graph

scholarly journals On the Genus of the Zero-Divisor Graph of Zn

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Huadong Su ◽  
Pailing Li
Keyword(s):  
Commutative Ring ◽  
Zero Divisor ◽  
Orientable Surface ◽  
Simple Graph ◽  
Ring Of Integers ◽  
Zero Divisor Graph ◽  
Zero Divisors

Let R be a commutative ring with identity. The zero-divisor graph of R, denoted Γ(R), is the simple graph whose vertices are the nonzero zero-divisors of R, and two distinct vertices x and y are linked by an edge if and only if xy=0. The genus of a simple graph G is the smallest integer g such that G can be embedded into an orientable surface Sg. In this paper, we determine that the genus of the zero-divisor graph of Zn, the ring of integers modulo n, is two or three.

scholarly journals On a new extension of the zero-divisor graph (II)

2021 ◽  
Author(s):  
A. Cherrabi ◽  
H. Essannouni ◽  
E. Jabbouri ◽  
A. Ouadfel
Keyword(s):  
Zero Divisor ◽  
Zero Divisor Graph

scholarly journals Sub-semigroups determined by the zero-divisor graph

2008 ◽  
Vol 308 (22) ◽  
pp. 5122-5135 ◽  
Author(s):  
Tongsuo Wu ◽  
Dancheng Lu
Keyword(s):  
Zero Divisor ◽  
Zero Divisor Graph
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