Results 91 to 100 of about 1,637,051 (209)

The Zero-Divisor Graphs of Variation Monogenic Semigroups

Scientific Journal of King Faisal University: Basic and Applied Sciences, 2020
The undirected graph Γ(〖VS〗_Mn) is the zero-divisor graph of the monogenic semigroup SM with zero. The non-zero vertices xi and xj of this graph are adjacent whenever i + j > n and gcd⁡(i,j)=1, where n is the order of Γ(〖VS〗_Mn).
Bana Jawid Al Subaiei, Abolape Deborah Akwu   +1 more
doaj   +1 more source

Zero-divisor graphs of idealizations

, 2006
We consider zero-divisor graphs of idealizations of commutative rings. Specifically, we look at the preservation, or lack thereof, of the diameter and girth of the zero-divisor graph of a ring when extending to idealizations of the ...
Stickles, Joe, Axtell, Michael
core   +1 more source

Adjacency spectra and Laplacian integrality of zero divisor graphs over some rings

Kuwait Journal of Science
Let 𝑅 be a commutative ring and let 𝑍∗ (𝑅) denote the set of non-zero zero divisors of 𝑅. The zero divisor graph 𝛤(𝑅) is defined as the simple graph with vertex set 𝑍∗ (𝑅), where two distinct vertices 𝑥, 𝑦 ∈ 𝑍∗ (𝑅) are adjacent if and only if 𝑥𝑦 = 0.
Bilal Ahmad Rather, Parvez Ali, M. Imran, A. Kothepeda   +3 more
doaj   +1 more source

Laplacian spectrum of weakly zero-divisor graph of the ring $\mathbb{Z}_{n}$

, 2023
Let $R$ be a commutative ring with unity. The weakly zero-divisor graph $W\Gamma(R)$ of the ring $R$ is the simple undirected graph whose vertices are nonzero zero-divisors of $R$ and two vertices $x$, $y$ are adjacent if and only if there exists $r\in {\
Mathil, Praveen, Shariq, Mohd, Kumar, Jitender   +2 more
core  

On the domination and signed domination numbers of zero-divisor graph

Electronic Journal of Graph Theory and Applications, 2016
Let $R$ be a commutative ring (with 1) and let $Z(R)$ be its set of zero-divisors. The zero-divisor graph $\Gamma(R)$ has vertex set $Z^*(R)=Z(R) \setminus \lbrace0 \rbrace$ and for distinct $x,y \in Z^*(R)$, the vertices $x$ and $y$ are adjacent if and ...
Ebrahim Vatandoost, Fatemeh Ramezani
doaj   +1 more source

A New Type of Zero Divisor Graphs of a Lattice, t-Zero Divisor Graphs

Turkish Journal of Mathematics and Computer Science
In this paper, we introduce the t-zero divisor graph $\Gamma_{T}(L)$, which is a generalization of the zero divisor graph of a lattice $\Gamma(L)$, where $t$ is a triangular norm on $L$. We investigate which properties hold in $t$-zero divisor graphs for special $t$-norms while giving some additional properties of the zero divisor graph.
openaire   +2 more sources

Induced subgraphs of zero-divisor graphs

, 2022
The zero-divisor graph of a finite commutative ring with unity is the graph whose vertex set is the set of zero-divisors in the ring, with $a$ and $b$ adjacent if $ab=0$. We show that the class of zero-divisor graphs is universal, in the sense that every
Chelvam, T. Tamizh, Arunkumar, G., Cameron, Peter J., Kavaskar, T.   +3 more
core  

On zero divisor graph of unique product monoid rings over Noetherian reversible ring [PDF]

Categories and General Algebraic Structures with Applications, 2016
Let $R$ be an associative ring with identity and $Z^*(R)$ be its set of non-zero zero divisors.  The zero-divisor graph of $R$, denoted by $Gamma(R)$, is the graph whose vertices are the non-zero  zero-divisors of  $R$, and two distinct vertices $r$ and $
Ebrahim Hashemi, Abdollah Alhevaz, Eshag Yoonesian   +2 more
doaj  

Generalized zero-divisor graph of ∗-rings

Asian-European Journal of Mathematics
A ∗-ring [Formula: see text] is a ring with an involution ∗. Let [Formula: see text] denote the set of all nonzero zero-divisors of [Formula: see text]. We associate a simple (undirected) graph [Formula: see text] with vertex set [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent in [Formula: see text]
Anita Lande, Anil Khairnar
openaire   +2 more sources

The zero divisor graph of 2 x 2 matrices over a field

, 2016
A zero divisor graph, Γ(R), is formed from a ring R by having each element of Z(R)\{0} to be a vertex in the graph and having two vertices u and v adjacent if the corresponding elements from the ring are nonequal and have product equal to zero.
Ashrafi, Ali Reza, Tadayyonfar, Adel
core