Results 191 to 200 of about 1,513 (227)
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2021
In this chapter, we study topological concepts like the genus of zero-divisor graphs. The prime objective of topological graph theory is to draw a graph on a surface so that no two edges cross, an intuitive geometric problem that can be enriched by specifying symmetries or combinatorial side-conditions.
David F. Anderson +3 more
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In this chapter, we study topological concepts like the genus of zero-divisor graphs. The prime objective of topological graph theory is to draw a graph on a surface so that no two edges cross, an intuitive geometric problem that can be enriched by specifying symmetries or combinatorial side-conditions.
David F. Anderson +3 more
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Distances in Zero-divisor Graphs
2021These concepts are the considerations of this chapter. Actually, we present results concerning the diameter, girth, and center of the zero-divisor graph of a commutative ring. We begin the chapter by introducing and discussing some basic concepts of the zero-divisor graph of a commutative ring.
David F. Anderson +3 more
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RECOVERING RINGS FROM ZERO-DIVISOR GRAPHS
Journal of Algebra and Its Applications, 2013Suppose G is the zero-divisor graph of some commutative ring with 1. When G has four or more vertices, a method is presented to find a specific commutative ring R with 1 such that Γ(R) ≅ G. Furthermore, this ring R can be written as R ≅ R1 × R2 × ⋯ × Rn, where each Ri is local and this representation of R is unique up to factors Ri with isomorphic ...
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On Realizing Zero-Divisor Graphs
Communications in Algebra, 2008An algorithm is presented for constructing the zero-divisor graph of a direct product of integral domains. Moreover, graphs which are realizable as zero-divisor graphs of direct products of integral domains are classified, as well as those of Boolean rings.
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A Characterization of Bipartite Zero-divisor Graphs
Canadian Mathematical Bulletin, 2014AbstractIn this paper we obtain a characterization for all bipartite zero-divisor graphs of commutative rings R with 1 such that R is finite or |Nil(R)| ≠ 2.
Rad, Nader Jafari, Jafari, Sayyed Heidar
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The Zero-Divisor Graph of a Lattice
Results in Mathematics, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Estaji, E., Khashyarmanesh, K.
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ZERO-DIVISOR GRAPHS OF ÖRE EXTENSION RINGS
Journal of Algebra and Its Applications, 2011Let R be an associative ring with two-sided multiplicative identity. In this paper, in the case that R is a commutative α-compatible ring, we compare the diameter (and girth) of the zero-divisor graphs Γ(R) and Γ(R[x;α, δ]). Moreover, we study the zero-divisors of the Öre extension ring R[x;α, δ], whenever R is reversible and (α, δ)-compatible.
Afkhami, M. +2 more
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Planar compressed zero-divisor graphs
Journal of Algebra and Its ApplicationsLet [Formula: see text] be a commutative ring. The relation on [Formula: see text] given by [Formula: see text] if and only if [Formula: see text] is an equivalence relation. The compressed zero-divisor graph, denoted by [Formula: see text], is the graph whose vertices are the equivalence classes induced by [Formula: see text] other than [Formula: see
Sheema Eydi +2 more
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Exact Decompositions and Zero-Divisor Graphs
Graphs and CombinatoricszbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Domination of zero-divisor graphs
Journal of Discrete Mathematical Sciences and CryptographyThe graph that has vertices as elements in a commutative ring R, such that u and v are adjacent only if uv = 0, is called the zero-divisor graph, Π(R). We study the domination of Π(Zn) for all parts of n in this study, since Zn is one of the well-known rings.
Haneen Al-Janabi +3 more
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