Results 41 to 50 of about 1,460,755 (212)
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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Electronic Notes in Discrete Mathematics, 2017 Abstract Let R be a finite commutative ring with unity ( 1 ≠ 0 ) and let Z ( R ) ⁎ be the set of non-zero zero-divisors of R. We associate a (simple) graph Γ ( R ) to R with vertices as elements of R and for distinct x , y ∈ R , the vertices x and y are adjacent if and only if xy = 0.
Deepa Sinha +2 more
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The Graph of Equivalence Classes of Zero Divisors [PDF]
ISRN Discrete Mathematics, 2014 We introduce a graph GE(L) of equivalence classes of zero divisors of a meet semilattice L with 0. The set of vertices of GE(L) are the equivalence classes of nonzero zero divisors of L and two vertices [x] and [y] are adjacent if and only if [x]∧[y]=[0]. It is proved that GE(L) is connected and either it contains a cycle of length 3 or GE(L)≅K2. It is
Vinayak Joshi +2 more
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Discrete Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Avinash Patil +2 more
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An ideal based zero-divisor graph of a commutative semiring [PDF]
, 2009 There is a natural graph associated to the zero-divisors of a commutative semiring with non-zero identity. In this article we essentially study zero-divisor graphs with respect to primal and non-primal ideals of a commutative semiring R and investigate ...
Ebrahimi Atani, Shahabaddin +1 more
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Some results on the total zero-divisor graph of a commutative ring [PDF]
Arab Journal of Mathematical SciencesPurposeThe purpose of this paper is to characterize a commutative ring R with identity which is not an integral domain such that ZT(R), the total zero-divisor graph of R is connected and to determine the diameter and radius of ZT(R) whenever ZT(R) is ...
Subramanian Visweswaran
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Zero divisor graphs of semigroups
Journal of Algebra, 2005 Let \(S\) be a commutative semigroup with \(0\). A simple graph \(G\) whose vertices are the nonzero zero divisors of \(S\) with two distinct vertices joined by an edge in case when their product in \(S\) is \(0\) is called the zero divisor graph of \(S\). In the paper some characterizations of graphs to be zero divisor graphs of a semigroup are given.
DeMeyer, Frank, DeMeyer, Lisa
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THE DOMINATION OF ZERO DIVISOR GRAPH ON THE LINE GRAPH [PDF]
, 2020 The directed Zero divisor graph is a graph constructed out of a non-Commutative ring R and its non-zero divisors. In this paper we find various domination parameter for the zero-divisor graph.
R, PREMKUMAR
core
On bipartite zero-divisor graphs
Discrete Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dancheng Lu, Tongsuo Wu
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When zero-divisor graphs are divisor graphs
TURKISH JOURNAL OF MATHEMATICS, 2017 Summary: Let \(R\) be a finite commutative principal ideal ring with unity. In this article, we prove that the zero-divisor graph \(\Gamma(R)\) is a divisor graph if and only if \(R\) is a local ring or it is a product of two local rings with at least one of them having diameter less than \(2\). We also prove that \(\Gamma(R)\) is a divisor graph.
Abu Osba, Emad, Alkam, Osama
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