Results 171 to 180 of about 1,637,051 (209)
On Domination in Zero-Divisor Graphs
Canadian Mathematical Bulletin, 2013 AbstractWe first determine the domination number for the zero-divisor graph of the product of two commutative rings with 1. We then calculate the domination number for the zero-divisor graph of any commutative artinian ring. Finally, we extend some of the results to non-commutative rings in which an element is a left zero-divisor if and only if it is a
Rad, Nader Jafari +2 more
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The Zero-Divisor Graph of a Lattice
Results in Mathematics, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Estaji, E., Khashyarmanesh, K.
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Chromatic uniqueness of zero-divisor graphs
The Art of Discrete and Applied Mathematics, 2022Summary: The zero-divisor graph \(\Pi(R)\) of a commutative ring \(R\) is the graph whose vertices are the elements of \(R\) such that the vertices \(u\) and \(v\) are adjacent if and only if \(uv=0\). If the graphs \(G\) and \(H\) have the same chromatic polynomial, then we say that they are chromatically equivalent (or \(\chi -\) equivalent), written
Haneen Al-Janabi, Gábor Bacsó
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The College Mathematics Journal, 2010
The last ten years have seen an explosion of research in the zero-divisor graphs of commutative rings—by professional mathematicians and undergraduates.
Axtell, Michael, Stickles, Joe
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The last ten years have seen an explosion of research in the zero-divisor graphs of commutative rings—by professional mathematicians and undergraduates.
Axtell, Michael, Stickles, Joe
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Zero-divisor super-$$\lambda$$ graphs
São Paulo Journal of Mathematical Sciences, 2022A maximally edge-connected graph with all minimum edge-cuts trivial is called super-\(\lambda\). In this paper, using the finite direct product of finite fields, the ring of the residues, and the trivial extension of rings by a module, the authors show that there are various classes of rings whose zero-divisor graphs are super-\(\lambda\) and then ...
Driss Bennis +2 more
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A Characterization of Bipartite Zero-divisor Graphs
Canadian Mathematical Bulletin, 2014AbstractIn this paper we obtain a characterization for all bipartite zero-divisor graphs of commutative rings R with 1 such that R is finite or |Nil(R)| ≠ 2.
Rad, Nader Jafari, Jafari, Sayyed Heidar
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The zero-divisor graphs of MV-algebras
Soft Computing, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aiping Gan, Yichuan Yang
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On zero divisor graphs of the rings $$Z_n$$
Afrika Matematika, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S. Pirzada, M. Aijaz, M. Imran Bhat
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The zero-divisor graph of a module
2017Summary: Let \(R\) be a commutative ring with identity and \(M\) an \(R\)-module. In this paper, we associate a graph to \(M\), say \(\Gamma (_{R}M)\), such that when \(M=R\), \(\Gamma (_{R}M)\) coincide with the zero-divisor graph of \(R\). Many well-known results by \textit{D. F. Anderson} and \textit{P. S. Livingston} [J. Algebra 217, No.
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