Results 31 to 40 of about 1,460,755 (212)
Distributive lattices and some related topologies in comparison with zero-divisor graphs [PDF]
Categories and General Algebraic Structures with Applications, 2021 In this paper,for a distributive lattice $\mathcal L$, we study and compare some lattice theoretic features of $\mathcal L$ and topological properties of the Stone spaces ${\rm Spec}(\mathcal L)$ and ${\rm Max}(\mathcal L)$ with the corresponding graph ...
Saeid Bagheri, mahtab Koohi Kerahroodi
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Comments on the Clique Number of Zero-Divisor Graphs of Zn
Journal of Mathematics, 2022 In 2008, J. Skowronek-kazio´w extended the study of the clique number ωGZn to the zero-divisor graph of the ring Zn, but their result was imperfect. In this paper, we reconsider ωGZn of the ring Zn and give some counterexamples. We propose a constructive
Yanzhao Tian, Lixiang Li
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On distance Laplacian spectrum of zero divisor graphs of the ring $\mathbb{Z}_{n}$
Karpatsʹkì Matematičnì Publìkacìï, 2021 For a finite commutative ring $\mathbb{Z}_{n}$ with identity $1\neq 0$, the zero divisor graph $\Gamma(\mathbb{Z}_{n})$ is a simple connected graph having vertex set as the set of non-zero zero divisors, where two vertices $x$ and $y$ are adjacent if and
S. Pirzada, B.A. Rather, T.A. Chishti
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The n-zero-divisor graph of a commutative semigroup
, 2022 Let S be a (multiplicative) commutative semigroup with 0, Z(S) the set of zero-divisors of S, and n a positive integer. The zero-divisor graph of S is the (simple) graph Γ(S) with vertices Z(S) ∗ = Z(S) \ {0}, and distinct vertices x and y are adjacent ...
Badawi, Ayman, Anderson, David F.
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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
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On graphs with equal coprime index and clique number
AKCE International Journal of Graphs and Combinatorics, 2023 Recently, Katre et al. introduced the concept of the coprime index of a graph. They asked to characterize the graphs for which the coprime index is the same as the clique number. In this paper, we partially solve this problem.
Chetan Patil +2 more
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STRUCTURE OF ZERO-DIVISOR GRAPHS ASSOCIATED TO RING OF INTEGER MODULO n [PDF]
Journal of Algebraic Systems, 2023 For a commutative ring $R$ with identity $1\neq 0$, let $Z^{*}(R)=Z(R)\setminus \lbrace 0\rbrace$ be the set of non-zero zero-divisors of $R$, where $Z(R)$ is the set of all zero-divisors of $R$.
Shariefuddin Pirzada +2 more
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THE ZERO-DIVISOR GRAPHS OF RINGS AND SEMIRINGS [PDF]
International Journal of Algebra and Computation, 2012 In this paper we study zero-divisor graphs of rings and semirings. We show that all zero-divisor graphs of (possibly noncommutative) semirings are connected and have diameter less than or equal to 3. We characterize all acyclic zero-divisor graphs of semirings and prove that in the case zero-divisor graphs are cyclic, their girths are less than or ...
David Dolzan, Polona Oblak
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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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Quotient Energy of Zero Divisor Graphs And Identity Graphs
مجلة بغداد للعلوم, 2023 Consider the (p,q) simple connected graph . The sum absolute values of the spectrum of quotient matrix of a graph make up the graph's quotient energy.
M. Lalitha Kumari +2 more
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