Results 21 to 30 of about 24,531 (183)

Upper dimension and bases of zero-divisor graphs of commutative rings

AKCE International Journal of Graphs and Combinatorics, 2020
For a commutative ring with non-zero zero divisor set , the zero divisor graph of is with vertex set , where two distinct vertices and are adjacent if and only if .
S. Pirzada, M. Aijaz, S.P. Redmond
doaj   +1 more source

On the eigenvalues of zero-divisor graph associated to finite commutative ring

AKCE International Journal of Graphs and Combinatorics, 2021
Let Z(R) be the set of zero-divisors of a commutative ring R with non-zero identity and be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by is a simple graph whose vertex set is and two vertices are adjacent if and only if ...
S. Pirzada, Bilal A. Wani, A. Somasundaram   +2 more
doaj   +1 more source

GENERALIZATIONS OF THE ZERO-DIVISOR GRAPH

International Electronic Journal of Algebra, 2020
Summary: Let \(R\) be a commutative ring with \(1\neq 0\) and \(Z(R)\) its set of zerodivisors. The zero-divisor graph of \(R\) is the (simple) graph \(\Gamma \)(R) with vertices \(Z(R) \backslash \{0\}\), and distinct vertices \(x\)and \(y\) are adjacent if and only if \(xy= 0\).
ANDERSON, David F., MCCLURKİN, Grace
openaire   +4 more sources

The k-Zero-Divisor Hypergraph of a Commutative Ring [PDF]

, 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.
A. M. Rahimi, Ch. Eslahchi
core   +4 more sources

A class of zero divisor rings in which every graph is precisely the union of a complete graph and a complete bipartite graph

Open Mathematics, 2015
Recently, an interest is developed in estimating genus of the zero-divisor graph of a ring. In this note we investigate genera of graphs of a class of zero-divisor rings (a ring in which every element is a zero divisor).
Nauman Syed Khalid, Shafee Basmah H.
doaj   +1 more source

Some results on the total zero-divisor graph of a commutative ring [PDF]

Arab Journal of Mathematical Sciences
PurposeThe purpose of this paper is to characterize a commutative ring R with identity which is not an integral domain such that ZT(R), the total zero-divisor graph of R is connected and to determine the diameter and radius of ZT(R) whenever ZT(R) is ...
Subramanian Visweswaran
doaj   +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

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

Classification of Zero Divisor Graphs of Commutative Rings of Degrees 11,12 and 13 [PDF]

Al-Rafidain Journal of Computer Sciences and Mathematics, 2014
In 2005  Wang investigated the zero divisor graphs of degrees 5,6,9 and 10. In 2012 Shuker and Mohammad investigated the zero divisor graphs of degrees 7 and 8. In this paper, we consider zero divisor graphs of commutative rings of degrees 11, 12 and 13.
Nazar Shuker, Husam Mohammad
doaj   +1 more source

Probabilistic characterizations of some finite ring of matrices and its zero divisor graph [PDF]

, 2020
Let R be a finite ring. In this study, the probability that two random elements chosen from a finite ring have product zero is determined for some finite ring of matrices over Zn.
Khasraw, Sanhan Muhammad Salih, Sarmin, Nor Haniza, Zaid, Nurhidayah   +2 more
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