Results 171 to 180 of about 24,531 (183)

The Zero-Divisor Graph of a Lattice

Results in Mathematics, 2010
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Estaji, E., Khashyarmanesh, K.
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ZERO-DIVISOR GRAPHS OF ÖRE EXTENSION RINGS

Journal of Algebra and Its Applications, 2011
Let R be an associative ring with two-sided multiplicative identity. In this paper, in the case that R is a commutative α-compatible ring, we compare the diameter (and girth) of the zero-divisor graphs Γ(R) and Γ(R[x;α, δ]). Moreover, we study the zero-divisors of the Öre extension ring R[x;α, δ], whenever R is reversible and (α, δ)-compatible.
Afkhami, M., Khashyarmanesh, K., Khorsandi, M. R.   +2 more
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Planar compressed zero-divisor graphs

Journal of Algebra and Its Applications
Let [Formula: see text] be a commutative ring. The relation on [Formula: see text] given by [Formula: see text] if and only if [Formula: see text] is an equivalence relation. The compressed zero-divisor graph, denoted by [Formula: see text], is the graph whose vertices are the equivalence classes induced by [Formula: see text] other than [Formula: see
Sheema Eydi, Mahdi Reza Khorsandi, Sayyed Heidar Jafari   +2 more
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Exact Decompositions and Zero-Divisor Graphs

Graphs and Combinatorics
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Domination of zero-divisor graphs

Journal of Discrete Mathematical Sciences and Cryptography
The graph that has vertices as elements in a commutative ring R, such that u and v are adjacent only if uv = 0, is called the zero-divisor graph, Π(R). We study the domination of Π(Zn) for all parts of n in this study, since Zn is one of the well-known rings.
Haneen Al-Janabi, Zainab Yasir Alrikabi, Haider Baqer Ameen, Shaymaa Maki Kadham   +3 more
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Infinite Planar Zero-Divisor Graphs

Communications in Algebra, 2006
Given a commutative ring R, one can associate with R an undirected graph Γ(R) whose vertices are the nonzero zero-divisors of R, and two distinct vertices x and y are joined by an edge iff xy = 0. In this article, we determine precisely those planar graphs that can be realized as Γ(R) when R is an infinite commutative ring.
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Zero-divisor Graph Generalizations

2021
David F. Anderson, T. Asir, Ayman Badawi, T. Tamizh Chelvam   +3 more
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Balanced zero-divisor graphs of matrix rings

Lobachevskii Journal of Mathematics, 2013
In this paper, the directed zero-divisor graph \(\Gamma (M_n(R))\) is studied. In particular it is proved that for a principal ideal commutative ring \(R\) with identity the directed zero-divisor graph \(\Gamma(M_n(R))\) is balanced and Eulerian.
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Analyzing special parameters over zero-divisor graphs

AIP Conference Proceedings, 2012
For different primes p and q, we prove some graph theoretical properties over the zero-divisor graph Γ(Zp×Zq) where R = Zp×Zq. Also we find the degree sequence, irregularity index, covering number, accessible number, atom-bound connectivity index and Wiener index of the zero-divisor graph of R.
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FINITE RINGS WITH EULERIAN ZERO-DIVISOR GRAPHS

Journal of Algebra and Its Applications, 2012
The zero-divisor graph Γ(R) of an associative ring R is the graph whose vertices are all non-zero (one-sided and two-sided) zero-divisors of R, and two distinct vertices x and y are joined by an edge if and only if xy = 0 or yx = 0. [S. P. Redmond, The zero-divisor graph of a noncommutative ring, Int. J. Commut.
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