Results 1 to 10 of about 575,168 (177)
Zero-divisor graphs and zero-divisor functors [PDF]
Journal of Algebra and Its Applications, 2023 Inspired by a very recent work of A. Đurić, S. Jevđenić and N. Stopar, we introduce a new definition of zero-divisor graphs attached to rings that includes all of the classical definitions already known in the literature. We provide an interpretation of such graphs by means of a functor that we call zero-divisor functor and which is associated with a ...
Enrico Sbarra, Maurizio Zanardo
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Zero-divisor ideals and realizable zero-divisor graphs [PDF]
Involve, a Journal of Mathematics, 2009 We seek to classify the sets of zero-divisors that form ideals based on their zero-divisor graphs. We offer full classification of these ideals within finite commutative rings with identity. We also provide various results concerning the realizability of a graph as a zero-divisor graph. 1.
Axtell, Michael +2 more
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A Zero Divisor Graph Determined by Equivalence Classes of Zero Divisors [PDF]
Communications in Algebra, 2011 We study the zero divisor graph determined by equivalence classes of zero divisors of a commutative Noetherian ring R. We demonstrate how to recover information about R from this structure. In particular, we determine how to identify associated primes from the graph.
Cameron Wickham
exaly +3 more sources
Upper dimension and bases of zero-divisor graphs of commutative rings
AKCE International Journal of Graphs and Combinatorics, 2020 For a commutative ring with non-zero zero divisor set , the zero divisor graph of is with vertex set , where two distinct vertices and are adjacent if and only if .
S. Pirzada, M. Aijaz, S.P. Redmond
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On the planarity of the k-zero-divisor hypergraphs
AKCE International Journal of Graphs and Combinatorics, 2015 Let R be a commutative ring with identity and let Z(R,k) be the set of all k-zero-divisors in R and k>2 an integer. The k-zero-divisor hypergraph of R, denoted by Hk(R), is a hypergraph with vertex set Z(R,k), and for distinct element x1,x2,…,xk in Z(R,k)
T. Tamizh Chelvam +2 more
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The wiener index of the zero-divisor graph for a new class of residue class rings
Frontiers in Chemistry, 2022 The zero-divisor graph of a commutative ring R, denoted by Γ(R), is a graph whose two distinct vertices x and y are joined by an edge if and only if xy = 0 or yx = 0.
Yinhu Wei, Ricai Luo
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Hardware acceleration of number theoretic transform for zk‐SNARK
Engineering Reports, EarlyView., 2023 An FPGA‐based hardware accelerator with a multi‐level pipeline is designed to support the large‐bitwidth and large‐scale NTT tasks in zk‐SNARK. It can be flexibly scaled to different scales of FPGAs and has been equipped in the heterogeneous acceleration system with the help of HLS and OpenCL.
Haixu Zhao +6 more
wiley +1 more source
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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Total perfect codes in graphs realized by commutative rings [PDF]
Transactions on Combinatorics, 2022 Let $R$ be a commutative ring with unity not equal to zero and let $\Gamma(R)$ be a zero-divisor graph realized by $R$. For a simple, undirected, connected graph $G = (V, E)$, a {\it total perfect code} denoted by $C(G)$ in $G$ is a subset $C(G ...
Rameez Raja
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Dynamic multi‐objective optimisation of complex networks based on evolutionary computation
IET Networks, EarlyView., 2022 Abstract As the problems concerning the number of information to be optimised is increasing, the optimisation level is getting higher, the target information is more diversified, and the algorithms are becoming more complex; the traditional algorithms such as particle swarm and differential evolution are far from being able to deal with this situation ...
Linfeng Huang
wiley +1 more source