Results 21 to 30 of about 1,513 (227)
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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Directed zero-divisor graph and skew power series rings [PDF]
Transactions on Combinatorics, 2018 Let $R$ be an associative ring with identity and $Z^{\ast}(R)$ be its set of non-zero zero-divisors. Zero-divisor graphs of rings are well represented in the literature of commutative and non-commutative rings. The directed zero-divisor graph of $R$
Ebrahim Hashemi +2 more
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Quotient Energy of Zero Divisor Graphs And Identity Graphs
مجلة بغداد للعلوم, 2023 Consider the (p,q) simple connected graph . The sum absolute values of the spectrum of quotient matrix of a graph make up the graph's quotient energy.
M. Lalitha Kumari +2 more
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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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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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Journal of Algebra, 2007 The authors answer two questions about zero divisor graphs posed by \textit{S.~Akbari, H. R.~Maimani} and \textit{S.~Yassemi} [J. Algebra 270, No. 1, 169--180 (2003; Zbl 1032.13014)] and \textit{D.~Anderson, A.~Frazier, A.~Lauve} and \textit{S.~Livingston} [Lect. Notes Pure Appl. Math. 220, 61--72 (2001; Zbl 1035.13004)], respectively.
Belshoff, Richard, Chapman, Jeremy
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GENERALIZATIONS OF THE ZERO-DIVISOR GRAPH
International Electronic Journal of Algebra, 2020 Summary: Let \(R\) be a commutative ring with \(1\neq 0\) and \(Z(R)\) its set of zerodivisors. The zero-divisor graph of \(R\) is the (simple) graph \(\Gamma \)(R) with vertices \(Z(R) \backslash \{0\}\), and distinct vertices \(x\)and \(y\) are adjacent if and only if \(xy= 0\).
ANDERSON, David F., MCCLURKİN, Grace
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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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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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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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