Results 21 to 30 of about 1,727 (183)
Zero-divisor ideals and realizable zero-divisor graphs [PDF]
Involve, a Journal of Mathematics, 2009 We seek to classify the sets of zero-divisors that form ideals based on their zero-divisor graphs. We offer full classification of these ideals within finite commutative rings with identity. We also provide various results concerning the realizability of a graph as a zero-divisor graph. 1.
Axtell, Michael +2 more
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Dynamic multi‐objective optimisation of complex networks based on evolutionary computation
IET Networks, EarlyView., 2022 Abstract As the problems concerning the number of information to be optimised is increasing, the optimisation level is getting higher, the target information is more diversified, and the algorithms are becoming more complex; the traditional algorithms such as particle swarm and differential evolution are far from being able to deal with this situation ...
Linfeng Huang
wiley +1 more source
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
doaj +1 more source
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
doaj +1 more source
Non Deterministic Zero Divisor Graph
Ratio Mathematica, 2023 A non-deterministic zero divisor graph refers to an element in a ring or algebraic structure that can multiply with another element to give zero, but the specific outcome of the multiplication is not uniquely determined.
Shakila Banu, Naveena Selvaraj
doaj +1 more source
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
doaj +1 more source
Rocky Mountain Journal of Mathematics, 2007 Let \(R\) be a commutative ring with unity. This paper studies \(Z(R)\) using homology group, where \(Z(R)\) is the set of zero-divisors in \(R\). In addition, the authors calculate the group \(H_{0}(R)\) in depth, in particular cases, and compute \(H_{1}(\frac{\mathbb{Z}}{p^{r}\mathbb{Z}})\) where \(p\) is a prime and \(r\geq 1\) is an integer.
Akhtar, Reza, Lee, Lucas
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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 +2 more
doaj +1 more source
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
doaj +1 more source
Graphs and Combinatorics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Richard H. Hammack, Heather C. Smith
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