Results 101 to 110 of about 88,527 (242)

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

Independent sets of some graphs associated to commutative rings

, 2013
Let $G=(V,E)$ be a simple graph. A set $S\subseteq V$ is independent set of $G$, if no two vertices of $S$ are adjacent. The independence number $\alpha(G)$ is the size of a maximum independent set in the graph.
Communicated A. R. Ashrafi, Saeed Mirvakili, Saeid Alikhani   +2 more
core   +1 more source

Signed Zero-Divisor Graph

Electronic Notes in Discrete Mathematics, 2017
Abstract Let R be a finite commutative ring with unity ( 1 ≠ 0 ) and let Z ( R ) ⁎ be the set of non-zero zero-divisors of R. We associate a (simple) graph Γ ( R ) to R with vertices as elements of R and for distinct x , y ∈ R , the vertices x and y are adjacent if and only if xy = 0.
Deepa Sinha, Deepakshi Sharma, Bableen Kaur   +2 more
openaire   +1 more source

The k-Zero-Divisor Hypergraph of a Commutative Ring

International Journal of Mathematics and Mathematical Sciences, 2007
The concept of the zero-divisor graph of a commutative ring has been studied by many authors, and the k-zero-divisor hypergraph of a commutative ring is a nice abstraction of this concept.
Ch. Eslahchi, A. M. Rahimi
doaj   +1 more source

Review of: "Zero-Divisor Graphs of ℤ_n, their products and D_n" [PDF]

, 2023
Imran Javaid
openalex   +3 more sources

Prime Rings with Involution Whose Symmetric Zero-Divisors are Nilpotent [PDF]

, 1973
P. M. Cohn
openalex   +1 more source

Perfect zero-divisor graphs

Discrete Mathematics, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Avinash Patil, B.N. Waphare, Vinayak Joshi   +2 more
openaire   +2 more sources

AN IDEAL - BASED ZERO-DIVISOR GRAPH OF POSETS [PDF]

, 2013
B. Elavarasan, K. Porselvi
openalex   +1 more source

Homogeneity of zero-divisors, units and colon ideals in a graded ring [PDF]

, 2021
Abolfazl Tarizadeh
openalex   +1 more source

Zero divisors of support size $3$ in group algebras and trinomials divided by irreducible polynomials over $GF(2)$

, 2019
A famous conjecture about group algebras of torsion-free groups states that there is no zero divisor in such group algebras. A recent approach to settle the conjecture is to show the non-existence of zero divisors with respect to the length of possible ...
Abdollahi, Alireza, Taheri, Zahra
core