Results 21 to 30 of about 830,410 (239)
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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A new additive function and the Smarandache divisor product sequences [PDF]
, 2009 The main purpose of this paper is using the elementary method and the prime distribution theory to study the mean value properties of G(n) in Smarandache divisor product sequences fpd(n)g and fqd(n)g, and give two sharper asymptotic formulae for ...
Weili, Yao +3 more
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Rocky Mountain Journal of Mathematics, 2007 Let \(R\) be a commutative ring with unity. This paper studies \(Z(R)\) using homology group, where \(Z(R)\) is the set of zero-divisors in \(R\). In addition, the authors calculate the group \(H_{0}(R)\) in depth, in particular cases, and compute \(H_{1}(\frac{\mathbb{Z}}{p^{r}\mathbb{Z}})\) where \(p\) is a prime and \(r\geq 1\) is an integer.
Akhtar, Reza, Lee, Lucas
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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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On the hybrid mean value of the Smarandache kn digital sequence with SL(n) function and divisor function d(n)1 [PDF]
, 2012 The main purpose of this paper is using the elementary method to study the hybrid mean value properties of the Smarandache kn digital sequence with SL(n) function and divisor function d(n), then give two interesting asymptotic formulae for ...
Le, Huan
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On graphs with equal coprime index and clique number
AKCE International Journal of Graphs and Combinatorics, 2023 Recently, Katre et al. introduced the concept of the coprime index of a graph. They asked to characterize the graphs for which the coprime index is the same as the clique number. In this paper, we partially solve this problem.
Chetan Patil +2 more
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Zero-divisor graphs of idealizations [PDF]
, 2006 We consider zero-divisor graphs of idealizations of commutative rings. Specifically, we look at the preservation, or lack thereof, of the diameter and girth of the zero-divisor graph of a ring when extending to idealizations of the ...
Stickles, J. +3 more
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Open Mathematics, 2015 Recently, an interest is developed in estimating genus of the zero-divisor graph of a ring. In this note we investigate genera of graphs of a class of zero-divisor rings (a ring in which every element is a zero divisor).
Nauman Syed Khalid, Shafee Basmah H.
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Graphs and Combinatorics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Richard H. Hammack, Heather C. Smith
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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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