Results 211 to 220 of about 22,120 (235)
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The First General Zagreb Index of the Zero Divisor Graph for the Ring Zpqk
Punjab University journal of mathematicsThis study investigates the application of graph theory in analyzing the zero divisor graph of a commutative ring, with a specific focus on its connection to the topological index. For an undirected graph Γ with consists of a non-empty set of vertices, V
G. S. Ismail +3 more
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Zero-divisors and zero-divisor graphs of power series rings [PDF]
Ricerche di Matematica, 2015 Let R be a commutative ring with identity, Z(R) its set of zero-divisors and N(R) its nilradical. The zero-divisor graph of R denoted by $$\varGamma (R)$$ , is the graph with vertices
Ali Benhissi, Amor Haouaoui
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On the Planar Property of an Ideal-Based Weakly Zero-Divisor Graph
Malaysian Journal of Fundamental and Applied SciencesLet R be a commutative ring with a nonzero identity and Z(R) be the set of zero-divisors of R. The weakly zero-divisor graph of R, denoted by WГ(R), is the graph with the vertex set 〖Z(R)〗^*=Z(R)\\{0}, where two distinct vertices a and b form an edge if ...
Asad Ghafoor +3 more
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Lobachevskii Journal of Mathematics, 2015
Let S always denote a semigroup with zero. This paper is devoted to study some of properties zero-divisor graph of S-act. We give several generalizations of the concept of zero-divisor elements in an S-act. Then for each S-act A we associate three undirected (simple) graphs Γ*(A) ⊆ Γ(A) ⊆ Γ*(A). Also we show that if A is an S-act, then (1) Γ*(A)
A. As. Estaji +2 more
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Let S always denote a semigroup with zero. This paper is devoted to study some of properties zero-divisor graph of S-act. We give several generalizations of the concept of zero-divisor elements in an S-act. Then for each S-act A we associate three undirected (simple) graphs Γ*(A) ⊆ Γ(A) ⊆ Γ*(A). Also we show that if A is an S-act, then (1) Γ*(A)
A. As. Estaji +2 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.
Abdeslam Mimouni, Salah-Eddine Kabbaj
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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.
T. Asir +3 more
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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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Exploring the Embedding of the Extended Zero-Divisor Graph of Commutative Rings
AxiomsRc represents commutative rings that have unity elements. The collection of all zero-divisor elements in Rc are represented by D(Rc). We denote an extended zero-divisor graph by the notation ℸ′(Rc) of Rc. This graph has a set of vertices in D(Rc)*.
Ali Al Khabyah, Moin A. Ansari
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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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Graph energy and topological descriptors of zero divisor graph associated with commutative ring
Journal of Applied Mathematics and Computation, 2023C. Johnson, Ravi Sankar
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