Results 1 to 10 of about 22,120 (235)
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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Applications on Topological Indices of Zero-Divisor Graph Associated with Commutative Rings [PDF]
Symmetry, 2023 A topological index is a numeric quantity associated with a chemical structure that attempts to link the chemical structure to various physicochemical properties, chemical reactivity, or biological activity. Let R be a commutative ring with identity, and
Clement Johnson Rayer, J. Ravi Sankar
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Zero Divisor Graph of Quotient Ring
Cauchy: Jurnal Matematika Murni dan AplikasiRecently, a lot of research has been carried out regarding graphs built from algebraic structures, including ring structures. One important example of a graph constructed from a ring is the zero divisor graph.
Ayunda Faizatul Musyarrofah +2 more
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Hyperideal-based zero-divisor graph of the general hyperring $ \mathbb{Z}_{n} $
AIMS MathematicsThe aim of this paper is to introduce and study the concept of a hyperideal-based zero-divisor graph associated with a general hyperring. This is a generalized version of the zero-divisor graph associated with a commutative ring.
Mohammad Hamidi, Irina Cristea
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On Domination in Zero-Divisor Graphs [PDF]
Canadian Mathematical Bulletin, 2011 AbstractWe first determine the domination number for the zero-divisor graph of the product of two commutative rings with 1. We then calculate the domination number for the zero-divisor graph of any commutative artinian ring. Finally, we extend some of the results to non-commutative rings in which an element is a left zero-divisor if and only if it is a
Nader Jafari Rad +2 more
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On zero-divisor graphs of finite rings
Journal of Algebra, 2007 AbstractThe zero-divisor graph of a ring R is defined as the directed graph Γ(R) that its vertices are all non-zero zero-divisors of R in which for any two distinct vertices x and y, x→y is an edge if and only if xy=0. Recently, it has been shown that for any finite ring R, Γ(R) has an even number of edges.
Saieed Akbari, A. Mohammadian
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On Normalized Laplacian Spectra of the Weakly Zero-Divisor Graph of the Ring ℤn
Mathematics, 2023 For a finite commutative ring R with identity 1≠0, the weakly zero-divisor graph of R denoted as WΓ(R) is a simple undirected graph having vertex set as a set of non-zero zero-divisors of R and two distinct vertices a and b are adjacent if and only if ...
Nazim, Nadeem Ur Rehman, Ahmad Alghamdi
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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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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 the diameter and girth of a zero-divisor graph
Journal of Pure and Applied Algebra, 2006 AbstractFor a commutative ring R with zero-divisors Z(R), the zero-divisor graph of R is Γ(R)=Z(R)−{0}, with distinct vertices x and y adjacent if and only if xy=0. In this paper, we characterize when either diam(Γ(R))≤2 or gr(Γ(R))≥4. We then use these results to investigate the diameter and girth for the zero-divisor graphs of polynomial rings, power
David F. Anderson, S. B. Mulay
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