Results 31 to 40 of about 1,233,365 (217)
Reduced zero-divisor graphs of posets [PDF]
Transactions on Combinatorics, 2018 This paper investigates properties of the reduced zero-divisor graph of a poset. We show that a vertex is an annihilator prime ideal if and only if it is adjacent to all other annihilator prime ideals and there are always two annihilator prime ideals ...
Deiborlang Nongsiang, Promode Saikia
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Discrete Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Avinash Patil +2 more
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Zero divisor graphs of semigroups
Journal of Algebra, 2005 Let \(S\) be a commutative semigroup with \(0\). A simple graph \(G\) whose vertices are the nonzero zero divisors of \(S\) with two distinct vertices joined by an edge in case when their product in \(S\) is \(0\) is called the zero divisor graph of \(S\). In the paper some characterizations of graphs to be zero divisor graphs of a semigroup are given.
DeMeyer, Frank, DeMeyer, Lisa
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Commutative rings with ideal based zero divisor graph of orders 12,13 and 14 [PDF]
Al-Rafidain Journal of Computer Sciences and MathematicsAn recent years, several studies have emerged on the graphs for commutative rings. Researchers have investigated ideal based zero-divisor graphs linked to commutative rings, delving into the characteristics of these graphs.
Raad Shukur, Husam Mohammad
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On a New Extension of the Zero-Divisor Graph [PDF]
Algebra Colloquium, 2020 In this paper, we introduce a new graph whose vertices are the non-zero zero-divisors of a commutative ring R, and for distincts elements x and y in the set Z(R)* of the non-zero zero-divisors of R, x and y are adjacent if and only if xy = 0 or x + y ∈ Z(R).
Cherrabi, A. +3 more
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Five Point Zero Divisor Graphs [PDF]
, 2010 We study the zero divisor graphs, determined by equivalence classes of zero divisors of a ring R. with exactly five vertices. In particular, we determine which graphs with exactly five vertices can be realized as the zero divisor graph of a ring.
Levidiotis, Florida Victoria
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Frequency Assignment Model of Zero Divisor Graph [PDF]
Journal of Applied Mathematics, 2021 Given a frequency assignment network model is a zero divisor graph Γ = V , E
R. Radha, N. Mohamed Rilwan
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Directed zero-divisor graph and skew power series rings [PDF]
Transactions on Combinatorics, 2018 Let $R$ be an associative ring with identity and $Z^{\ast}(R)$ be its set of non-zero zero-divisors. Zero-divisor graphs of rings are well represented in the literature of commutative and non-commutative rings. The directed zero-divisor graph of $R$
Ebrahim Hashemi +2 more
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On determining number and metric dimension of zero-divisor graphs [PDF]
, 2023 In this article, explicit formulas for finding the determining number and the metric dimension of the zero-divisor graph of Z_n and non-Boolean semisimple rings are given.
K, Muhammed Sabeel +1 more
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Group Action on the Set of Nonunits in Rings
Journal of Mathematics, 2023 Let R be a ring, G be the group of all units of R, and X=R−G∪0. In this paper, we investigate avxx∈X=oxx∈X for a ring R, where avx is the set of all vertices of the zero-divisor graph of R adjacent to x.
Eman S. Almotairi +2 more
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