Results 1 to 10 of about 7,874 (214)
The Zero Divisor Graph of the Ring Zqp.
Science Journal of University of Zakho, 2015 In this paper we construct a star zero divisor graph from the zero divisor graph of the ring Zqp. The star zero divisor graph is obtained by removing some vertices from the zero divisor graph Γ(Zqp), in different ways , but the best way to get star zero ...
Nazar H. Shuker, Payman A. Rashed
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The wiener index of the zero-divisor graph for a new class of residue class rings [PDF]
Frontiers in Chemistry, 2022 The zero-divisor graph of a commutative ring R, denoted by Γ(R), is a graph whose two distinct vertices x and y are joined by an edge if and only if xy = 0 or yx = 0.
Yinhu Wei, Ricai Luo
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Harary index of the zero divisor graph of upper triangular matrices [PDF]
Scientific ReportsThe Harary Index is an important topological parameter for examining the structure of a graph. This work presents a quantitative analysis of the structural features of zero-divisor graph using the Harary Index.
Omaima Alshanqiti +2 more
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A Zero Divisor Graph Determined by Equivalence Classes of Zero Divisors [PDF]
Communications in Algebra, 2011 We study the zero divisor graph determined by equivalence classes of zero divisors of a commutative Noetherian ring R. We demonstrate how to recover information about R from this structure. In particular, we determine how to identify associated primes from the graph.
Cameron Wickham
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A graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs [PDF]
HeliyonThis article investigates the concept of dominant metric dimensions in zero divisor graphs (ZD-graphs) associated with rings. Consider a finite commutative ring with unity, denoted as R, where nonzero elements x and y are identified as zero divisors if ...
Nasir Ali +4 more
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A Study on the Structure of Ideal-Based Non-Zero Divisor Graphs Associated with Zn [version 1; peer review: 2 approved] [PDF]
F1000ResearchBackground The study of algebraic structures through graph-theoretic representations provides a powerful visual and combinatorial framework for analyzing ring-theoretic properties. The ideal-based non-zero divisor graph ∅ I ( Z n ) , constructed from the
Ali Abd Aubad, Sameer Kadem
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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 of commutative ring Rη, in this model, each node is considered to be a channel and their labelings are said to be the frequencies, which are assigned by the L2,1 and L3,2,1 labeling
R. Radha, N. Mohamed Rilwan
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On generalized zero divisor graph of a poset
Discrete Applied Mathematics, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vinayak Joshi
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Zero-divisor graphs and zero-divisor functors
Journal of Algebra and Its Applications, 2023 Inspired by a very recent work of A. Đurić, S. Jevđenić and N. Stopar, we introduce a new definition of zero-divisor graphs attached to rings that includes all of the classical definitions already known in the literature. We provide an interpretation of such graphs by means of a functor that we call zero-divisor functor and which is associated with a ...
Enrico Sbarra, Maurizio Zanardo
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Total perfect codes in graphs realized by commutative rings [PDF]
Transactions on Combinatorics, 2022 Let $R$ be a commutative ring with unity not equal to zero and let $\Gamma(R)$ be a zero-divisor graph realized by $R$. For a simple, undirected, connected graph $G = (V, E)$, a {\it total perfect code} denoted by $C(G)$ in $G$ is a subset $C(G ...
Rameez Raja
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