Results 11 to 20 of about 7,874 (214)
Non Deterministic Zero Divisor Graph [PDF]
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
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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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Zero Divisor Graph of Quotient Ring [PDF]
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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Induced subgraphs of zero-divisor graphs [PDF]
Discrete Mathematics, 2023 The zero-divisor graph of a finite commutative ring with unity is the graph whose vertex set is the set of zero-divisors in the ring, with $a$ and $b$ adjacent if $ab=0$. We show that the class of zero-divisor graphs is universal, in the sense that every finite graph is isomorphic to an induced subgraph of a zero-divisor graph.
G. Arunkumar +3 more
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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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A note on the zero divisor graph of a lattice [PDF]
Transactions on Combinatorics, 2014 Let $L$ be a lattice with the least element $0$. An element $xin L$ is a zero divisor if $xwedge y=0$ for some $yin L^*=Lsetminus left{0right}$. The set of all zero divisors is denoted by $Z(L)$.
T. Tamizh Chelvam , S. Nithya
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Note on Ideal Based Zero-Divisor Graph of a Commutative Ring
Discussiones Mathematicae - General Algebra and Applications, 2017 In this paper, we consider the ideal based zero divisor graph ΓI(R) of a commutative ring R. We discuss some graph theoretical properties of ΓI(R) in relation with zero divisor graph.
Mallika A., Kala R., Selvakumar K.
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Open Mathematics, 2015 Recently, an interest is developed in estimating genus of the zero-divisor graph of a ring. In this note we investigate genera of graphs of a class of zero-divisor rings (a ring in which every element is a zero divisor).
Nauman Syed Khalid, Shafee Basmah H.
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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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Some results on the total zero-divisor graph of a commutative ring [PDF]
Arab Journal of Mathematical SciencesPurposeThe purpose of this paper is to characterize a commutative ring R with identity which is not an integral domain such that ZT(R), the total zero-divisor graph of R is connected and to determine the diameter and radius of ZT(R) whenever ZT(R) is ...
Subramanian Visweswaran
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