Results 111 to 120 of about 1,397,791 (213)

Planar Zero-Divisor Graphs

, 2006
Associated to every nonzero commutative ring with identity is a graph whose vertices are the nonzero zero-divisors, and such that two distinct vertices x and y are adjacent if and only if xy = 0.
Chapman, Jeremy M.
core  

Randić spectrum of the weakly zero-divisor graph of the ring ℤn

AKCE International Journal of Graphs and Combinatorics
In this article, we find the Randić spectrum of the weakly zero-divisor graph of a finite commutative ring [Formula: see text] with identity [Formula: see text], denoted as [Formula: see text], where [Formula: see text] is taken as the ring of integers ...
Nadeem Ur Rehman, Nazim, Ahmad M. Alghamdi, Eman S. Almotairi   +3 more
doaj   +1 more source

Laplacian Energy and Eccentricity Based Energy for Cross Monic Zero Divisor Graph Associated With Commutative Rings

مجلة بغداد للعلوم
For a commutative ring, a cross monic zero divisor graph is discussed, whose vertices are nonzero zero divisors of the commutative ring, then the two vertices x and y are adjacent if and only if xy = 0.
Sarathy Raja, Ravi Sankar Jeyaraj
doaj   +1 more source

Zero-divisor graphs of reduced Rickart *-rings

Discussiones Mathematicae - General Algebra and Applications, 2017
For a ring A with an involution *, the zero-divisor graph of A, Γ*(A), is the graph whose vertices are the nonzero left zero-divisors in A such that distinct vertices x and y are adjacent if and only if xy* = 0.
Patil A.A., Waphare B.N.
doaj   +1 more source

Generalizations of the Zero-Divisor Graph of a Ring [PDF]

, 2001
Let R be a commutative ring with 1, and let Z(R) denote the set of zero­divisors of R. We define an undirected graph Γ(R) with vertices Z(R)* = Z(R) - {0}, where distinct vertices x and y of R are connected if and only if xy = 0. This graph is called the
Redmond, Shane Patrick
core  

The zero-divisor graph of an amalgamated algebra [PDF]

Let $R$ and $S$ be commutative rings with identity, $f:R\to S$ a ring homomorphism and $J$ an ideal of $S$. Then the subring $R\bowtie^fJ:=\{(r,f(r)+j)\mid r\in R$ and $j\in J\}$ of $R\times S$ is called the amalgamation of $R$ with $S$ along $J$ with ...
Doustimehr, M. R., Azimi, Y.
core   +1 more source

Graphs from matrices - a survey

AKCE International Journal of Graphs and Combinatorics
Let R be a commutative ring with identity. For a positive integer [Formula: see text] let [Formula: see text] be the set of all n × n matrices over R and [Formula: see text] be the set of all non-zero matrices of [Formula: see text] The zero-divisor ...
T. Tamizh Chelvam
doaj   +1 more source

On zero-divisor graphs of infinite posets

Soft Computing
AbstractIt is known that the so-called Beck’s conjecture, i.e. the equality of the finite clique and chromatic numbers of a zero-divisor graph, holds for partially ordered sets Halaš and Jukl (Discrete Math 309(13):4584–4589, 2009). In this paper we present a simple direct proof of this fact.
Radomír Halas, Jozef Pócs
openaire   +1 more source

Graph Operations on Zero-Divisor Graph of Posets

, 2018
We know that some large graphs can be constructed from some smaller graphs by using graphs operations. Many properties of such large graphs are closely related to those of the corresponding smaller ones.
N. Hosseinzadeh (5758513)
core   +1 more source

Properties of ideal-based zero-divisor graphs of commutative rings [PDF]

, 2014
Let R be a commutative ring with nonzero identity and I an ideal of R. The focus of this research is on a generalization of the zero-divisor graph called the ideal-based zero-divisor graph for commutative rings with nonzero identity.
Jesse Gerald Smith, Jr., Smith, Jesse Gerald, Jr.   +1 more
core