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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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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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Simple Graphs and Zero-divisor Semigroups
Algebra Colloquium, 2009In this paper, we provide examples of graphs which uniquely determine a zero-divisor semigroup. We show two classes of graphs that have no corresponding semigroups. Especially, we prove that no complete r-partite graph together with two or more end vertices (each linked to distinct vertices) has corresponding semigroups.
Wu, Tongsuo, Chen, Li
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On the zero-divisor graph of Rickart *-rings
Asian-European Journal of Mathematics, 2017In this paper, we study the zero-divisor graph of Rickart *-rings. We determine the condition on Rickart *-ring so that its zero-divisor graph contains a cut vertex. It is proved that the set of cut vertices form a complete subgraph. We characterize Rickart *-rings for which the complement of the zero-divisor graph is connected. The diameter and girth
Patil, Avinash, Waphare, B. N.
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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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Lobachevskii Journal of Mathematics, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Estaji, A. A. +2 more
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Estaji, A. A. +2 more
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Acta Mathematica Hungarica, 2005
As usual, let \(C(X)\) denote the ring of all real-valued continuous functions on a Tychonoff space \(X\). By the zero-divisor graph \(\Gamma (C(X))\) of \(C(X)\) we mean the graph with vertices nonzero zero-divisors of \(C(X)\) such that there is an edge between vertices \(f\), \(g\) if and only if \(f\neq g\) and \(fg=0\).
Azarpanah, F., Motamedi, M.
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As usual, let \(C(X)\) denote the ring of all real-valued continuous functions on a Tychonoff space \(X\). By the zero-divisor graph \(\Gamma (C(X))\) of \(C(X)\) we mean the graph with vertices nonzero zero-divisors of \(C(X)\) such that there is an edge between vertices \(f\), \(g\) if and only if \(f\neq g\) and \(fg=0\).
Azarpanah, F., Motamedi, M.
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Zero-divisors and zero-divisor graphs of power series rings
Ricerche di Matematica, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Haouaoui, Amor, Benhissi, Ali
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2021
In this chapter, we study topological concepts like the genus of zero-divisor graphs. The prime objective of topological graph theory is to draw a graph on a surface so that no two edges cross, an intuitive geometric problem that can be enriched by specifying symmetries or combinatorial side-conditions.
David F. Anderson +3 more
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In this chapter, we study topological concepts like the genus of zero-divisor graphs. The prime objective of topological graph theory is to draw a graph on a surface so that no two edges cross, an intuitive geometric problem that can be enriched by specifying symmetries or combinatorial side-conditions.
David F. Anderson +3 more
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