Results 201 to 210 of about 22,120 (235)
The Zero-Divisor Graph of a Lattice [PDF]
Results in Mathematics, 2010 For a finite bounded lattice £, we associate a zero-divisor graph G(£) which is a natural generalization of the concept of zero-divisor graph for a Boolean algebra. Also, we study the interplay of lattice-theoretic properties of £ with graph-theoretic properties of G(£).
Ehsan Estaji, Kazem Khashyarmanesh
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The Wiener Index and the Wiener Complexity of the Zero-Divisor Graph of a Finite Semisimple Ring
Social Science Research Network, 2023A BSTRACT . We calculate the Wiener index of the zero-divisor graph of a finite semisimple ring. We also calculate the Wiener complexity of the zero-divisor graph of a finite simple ring and find an upper bound for the Wiener complexity in the semisimple ...
David Dolžan
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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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On the Zero-Divisor Graph of a Ring [PDF]
Communications in Algebra, 2008 Let R be a commutative ring with identity, Z(R) its set of zero-divisors, and Nil(R) its ideal of nilpotent elements. 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 article, we study Γ(R) for rings R with nonzero zero-divisors which satisfy certain divisibility conditions between ...
David F. Anderson, Ayman Badawi
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The Diameter of a Zero-Divisor Graph for Finite Direct Product of Commutative Rings
Sarajevo Journal of MathematicsThis paper establishes a set of theorems that describe the diameter of a zero-divisor graph for a finite direct product$R_{1}\times R_{2}\times\cdots\times R_{n}$ with respect to the diameters of the zero-divisor graphs of $R_{1},R_{2},\cdots,R_{n-1 ...
S. E. Atani, M. Kohan
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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.
Pranjali +3 more
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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.
T. Asir +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.
T. Asir +3 more
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Intervals of posets of a zero-divisor graph
Mathematica SlovacaThis article is concerned with bounded partially ordered sets P such that for every p ∈ P ∖ {1} there exists q ∈ P ∖ {0} such that 0 is the only lower bound of {p, q}.
John D. LaGrange
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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.
T. Asir +3 more
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Generalized Zero-divisor Graphs
2021The zero-divisor graph of a commutative ring has been generalized by several authors. The two most notable generalizations are the ideal-based zero-divisor graph and annihilating-ideal graph of commutative rings. We first discuss the ideal-based zero-divisor graph of a commutative ring.
Ayman Badawi +3 more
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