Results 21 to 30 of about 1,283,848 (178)
Non Deterministic Zero Divisor Graph
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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Comments on the Clique Number of Zero-Divisor Graphs of Zn
Journal of Mathematics, 2022 In 2008, J. Skowronek-kazio´w extended the study of the clique number ωGZn to the zero-divisor graph of the ring Zn, but their result was imperfect. In this paper, we reconsider ωGZn of the ring Zn and give some counterexamples. We propose a constructive
Yanzhao Tian, Lixiang Li
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Wiener index of graphs over rings: a survey
AKCE International Journal of Graphs and Combinatorics, 2022 This article presents a survey of results consisting of the Wiener index of graphs associated with commutative rings. In particular, we focus on zero-divisor graphs, unit graphs, total graphs and prime graphs.
T. Asir +3 more
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On distance Laplacian spectrum of zero divisor graphs of the ring $\mathbb{Z}_{n}$
Karpatsʹkì Matematičnì Publìkacìï, 2021 For a finite commutative ring $\mathbb{Z}_{n}$ with identity $1\neq 0$, the zero divisor graph $\Gamma(\mathbb{Z}_{n})$ is a simple connected graph having vertex set as the set of non-zero zero divisors, where two vertices $x$ and $y$ are adjacent if and
S. Pirzada, B.A. Rather, T.A. Chishti
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Classification of Genus Three Zero-Divisor Graphs
, 2023 In this paper, we consider the problem of classifying commutative rings according to the genus number of its associating zero-divisor graphs. The zero-divisor graph of R, where R is a commutative ring with nonzero identity, denoted by Γ(R), is the ...
Turki Alsuraiheed +2 more
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Distances in zero-divisor and total graphs from commutative rings–A survey
AKCE International Journal of Graphs and Combinatorics, 2016 There are so many ways to construct graphs from algebraic structures. Most popular constructions are Cayley graphs, commuting graphs and non-commuting graphs from finite groups and zero-divisor graphs and total graphs from commutative rings.
T. Tamizh Chelvam, T. Asir
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Exploring the properties of the zero-divisor graph of direct product of $\ast$-rings [PDF]
Journal of Mahani Mathematical ResearchIn this paper, we delve into the study of zero-divisor graphs in rings equipped with an involution. Specifically, we focus on abelian Rickart $\ast$-rings.
Mohd Nazim +2 more
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Mathematics, 2023 The field of mathematics that studies the relationship between algebraic structures and graphs is known as algebraic graph theory. It incorporates concepts from graph theory, which examines the characteristics and topology of graphs, with those from ...
Amal S. Alali +5 more
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On the eigenvalues of zero-divisor graph associated to finite commutative ring
AKCE International Journal of Graphs and Combinatorics, 2021 Let Z(R) be the set of zero-divisors of a commutative ring R with non-zero identity and be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by is a simple graph whose vertex set is and two vertices are adjacent if and only if ...
S. Pirzada +2 more
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Reduced zero-divisor graphs of posets [PDF]
Transactions on Combinatorics, 2018 This paper investigates properties of the reduced zero-divisor graph of a poset. We show that a vertex is an annihilator prime ideal if and only if it is adjacent to all other annihilator prime ideals and there are always two annihilator prime ideals ...
Deiborlang Nongsiang, Promode Saikia
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