Results 201 to 210 of about 1,513 (227)
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Infinite Planar Zero-Divisor Graphs
Communications in Algebra, 2006Given a commutative ring R, one can associate with R an undirected graph Γ(R) whose vertices are the nonzero zero-divisors of R, and two distinct vertices x and y are joined by an edge iff xy = 0. In this article, we determine precisely those planar graphs that can be realized as Γ(R) when R is an infinite commutative ring.
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Balanced zero-divisor graphs of matrix rings
Lobachevskii Journal of Mathematics, 2013In this paper, the directed zero-divisor graph \(\Gamma (M_n(R))\) is studied. In particular it is proved that for a principal ideal commutative ring \(R\) with identity the directed zero-divisor graph \(\Gamma(M_n(R))\) is balanced and Eulerian.
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Analyzing special parameters over zero-divisor graphs
AIP Conference Proceedings, 2012For different primes p and q, we prove some graph theoretical properties over the zero-divisor graph Γ(Zp×Zq) where R = Zp×Zq. Also we find the degree sequence, irregularity index, covering number, accessible number, atom-bound connectivity index and Wiener index of the zero-divisor graph of R.
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FINITE RINGS WITH EULERIAN ZERO-DIVISOR GRAPHS
Journal of Algebra and Its Applications, 2012The zero-divisor graph Γ(R) of an associative ring R is the graph whose vertices are all non-zero (one-sided and two-sided) zero-divisors of R, and two distinct vertices x and y are joined by an edge if and only if xy = 0 or yx = 0. [S. P. Redmond, The zero-divisor graph of a noncommutative ring, Int. J. Commut.
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Engineered platforms for topological superconductivity and Majorana zero modes
Nature Reviews Materials, 2021Karsten Flensberg +2 more
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Zero-Dimensional Carbon Nanomaterials for Fluorescent Sensing and Imaging
Chemical Reviews, 2023Zheng Yang, Meng-Yao She, Jiao Chen
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Recent progress of zero-dimensional luminescent metal halides
Chemical Society Reviews, 2021Zhiguo Xia
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