Results 181 to 190 of about 1,513 (227)
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The College Mathematics Journal, 2010
The last ten years have seen an explosion of research in the zero-divisor graphs of commutative rings—by professional mathematicians and undergraduates.
Axtell, Michael, Stickles, Joe
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The last ten years have seen an explosion of research in the zero-divisor graphs of commutative rings—by professional mathematicians and undergraduates.
Axtell, Michael, Stickles, Joe
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Simple Graphs and Zero-divisor Semigroups
Algebra Colloquium, 2009In this paper, we provide examples of graphs which uniquely determine a zero-divisor semigroup. We show two classes of graphs that have no corresponding semigroups. Especially, we prove that no complete r-partite graph together with two or more end vertices (each linked to distinct vertices) has corresponding semigroups.
Wu, Tongsuo, Chen, Li
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Journal of Algebra and Its Applications, 2020
Let [Formula: see text] be a commutative ring and [Formula: see text] be the zero divisor graph of [Formula: see text]. In this paper, we investigate when the zero divisor graph is a line graph. We completely present all commutative rings which their zero divisor graphs are line graphs. Also, we study when the zero divisor graph is the complement of a
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Let [Formula: see text] be a commutative ring and [Formula: see text] be the zero divisor graph of [Formula: see text]. In this paper, we investigate when the zero divisor graph is a line graph. We completely present all commutative rings which their zero divisor graphs are line graphs. Also, we study when the zero divisor graph is the complement of a
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Acta Mathematica Hungarica, 2005
As usual, let \(C(X)\) denote the ring of all real-valued continuous functions on a Tychonoff space \(X\). By the zero-divisor graph \(\Gamma (C(X))\) of \(C(X)\) we mean the graph with vertices nonzero zero-divisors of \(C(X)\) such that there is an edge between vertices \(f\), \(g\) if and only if \(f\neq g\) and \(fg=0\).
Azarpanah, F., Motamedi, M.
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As usual, let \(C(X)\) denote the ring of all real-valued continuous functions on a Tychonoff space \(X\). By the zero-divisor graph \(\Gamma (C(X))\) of \(C(X)\) we mean the graph with vertices nonzero zero-divisors of \(C(X)\) such that there is an edge between vertices \(f\), \(g\) if and only if \(f\neq g\) and \(fg=0\).
Azarpanah, F., Motamedi, M.
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Lobachevskii Journal of Mathematics, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Estaji, A. A. +2 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Estaji, A. A. +2 more
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Zero-divisors and zero-divisor graphs of power series rings
Ricerche di Matematica, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Haouaoui, Amor, Benhissi, Ali
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Signed Zero-Divisor Graphs Over Commutative Rings
Communications in Mathematics and Statistics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lu Lu, Lihua Feng, Weijun Liu
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Properties of Zero-divisor Graphs
2021In this chapter, we deal with some graph-theoretical properties of the zero-divisor graph of a commutative ring such as colorings, connectedness, bipartite nature, isomorphisms, and automorphisms.
David F. Anderson +3 more
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Zero-divisor Labelings of Graphs
Communications in Algebra, 2016This paper introduces the notions of a zero-divisor labeling and the zero-divisor index of a graph using the zero-divisors of a commutative ring. Viewed in this way, the usual zero-divisor graph is a maximal graph with respect to a zero-divisor labeling. We also study optimal zero-divisor labelings of a finite graph.
null Pranjali +3 more
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Zero-divisor graphs of amalgamations
MATHEMATICA SCANDINAVICA, 2018Let $f\colon A\rightarrow B$ be a homomorphism of commutative rings and let $J$ be an ideal of $B$. The amalgamation of $A$ with $B$ along $J$ with respect to $f$ is the subring of $A\times B$ given by \[ A\bowtie ^{f}J:=\{(a,f(a)+j) \mid a\in A, j\in J\}. \] This paper investigates the zero-divisor graph of amalgamations.
Salah-Eddine Kabbaj, Abdeslam Mimouni
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