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Boxicity of Zero Divisor Graphs
CoRRA $d$-dimensional box is the cartesian product $R_i\times\cdots\times R_d$ where each $R_i$ is a closed interval on the real line. The boxicity of a graph, denoted as $box(G)$, is the minimum integer $d\geq 0$ such that $G$ is the intersection graph of a collection of $d$-dimensional boxes.
L. Sunil Chandran, Suraj Kumar Sahoo
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Fault-tolerant metric dimension of zero-divisor graphs of commutative rings
AKCE International Journal of Graphs and Combinatorics, 2021 Let R be a commutative ring with identity. The zero-divisor graph of R denoted by is an undirected graph where is the set of non-zero zero-divisors of R and there is an edge between the vertices z1 and z2 in if A set of vertices S resolves a graph G if ...
Sahil Sharma, Vijay Kumar Bhat
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Noûs, EarlyView.ABSTRACT It is a truism of mathematics that differences between isomorphic number systems are irrelevant to arithmetic. This truism is deeply rooted in the modern axiomatic method and underlies most strands of arithmetical structuralism, the view that arithmetic is about some abstract number structure.
Balthasar Grabmayr
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The total zero-divisor graph of commutative rings
, 2018 In this paper we initiate the study of the total zero-divisor graphs over commutative rings with unity. These graphs are constructed by both relations that arise from the zero-divisor graph and from the total graph of a ring.
Đurić, Alen +3 more
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On the additive image of zeroth persistent homology
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract For a category X$X$ and a finite field F$F$, we study the additive image of the functor H0(−;F)∗:rep(X,Top)→rep(X,VectF)$\operatorname{H}_0(-;F)_* \colon \operatorname{rep}(X, \mathbf {Top}) \rightarrow \operatorname{rep}(X, \mathbf {Vect}_F)$, or equivalently, of the free functor rep(X,Set)→rep(X,VectF)$\operatorname{rep}(X, \mathbf {Set ...
Ulrich Bauer +3 more
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Commutative rings with ideal based zero divisor graph of orders 12,13 and 14 [PDF]
Al-Rafidain Journal of Computer Sciences and MathematicsAn recent years, several studies have emerged on the graphs for commutative rings. Researchers have investigated ideal based zero-divisor graphs linked to commutative rings, delving into the characteristics of these graphs.
Raad Shukur, Husam Mohammad
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COMPLEMENT OF THE ZERO DIVISOR GRAPH OF A LATTICE [PDF]
Bulletin of the Australian Mathematical Society, 2013 AbstractIn this paper, we determine when $\mathop{({\Gamma }_{I} (L))}\nolimits ^{c} $, the complement of the zero divisor graph ${\Gamma }_{I} (L)$ with respect to a semiprime ideal $I$ of a lattice $L$, is connected and also determine its diameter, radius, centre and girth. Further, a form of Beck’s conjecture is proved for ${\Gamma }_{I} (L)$ when $\
Joshi, Vinayak, Khiste, Anagha
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On the Foundational Arguments of Sufficient Dimension Reduction
WIREs Computational Statistics, Volume 18, Issue 2, June 2026.Contemporary Sufficient Dimension Reduction, a versatile method for extracting material information from data, can serve as a preprocessor for classical modeling and inference, or as a standalone theory that leads directly to statistical inference. ABSTRACT Sufficient dimension reduction (SDR) refers to supervised methods of dimension reduction that ...
R. Dennis Cook
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Local Rings with Genus Two Zero Divisor Graph
, 2010 To each commutative ring R we can associate a graph, the zero divisor graph of R, whose vertices are the zero divisors of R, and such that two vertices are adjacent if their product is zero.
Bloomfield, Nathan +3 more
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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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