Results 81 to 90 of about 600 (179)
Adjacency spectra and Laplacian integrality of zero divisor graphs over some rings
Kuwait Journal of ScienceLet ๐ be a commutative ring and let ๐โ (๐ ) denote the set of non-zero zero divisors of ๐ . The zero divisor graph ๐ค(๐ ) is defined as the simple graph with vertex set ๐โ (๐ ), where two distinct vertices ๐ฅ, ๐ฆ โ ๐โ (๐ ) are adjacent if and only if ๐ฅ๐ฆ = 0.
Bilal Ahmad Rather +3 more
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On the domination and signed domination numbers of zero-divisor graph
Electronic Journal of Graph Theory and Applications, 2016 Let $R$ be a commutative ring (with 1) and let $Z(R)$ be its set of zero-divisors. The zero-divisor graph $\Gamma(R)$ has vertex set $Z^*(R)=Z(R) \setminus \lbrace0 \rbrace$ and for distinct $x,y \in Z^*(R)$, the vertices $x$ and $y$ are adjacent if and ...
Ebrahim Vatandoost, Fatemeh Ramezani
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A New Type of Zero Divisor Graphs of a Lattice, t-Zero Divisor Graphs
Turkish Journal of Mathematics and Computer ScienceIn this paper, we introduce the t-zero divisor graph $\Gamma_{T}(L)$, which is a generalization of the zero divisor graph of a lattice $\Gamma(L)$, where $t$ is a triangular norm on $L$. We investigate which properties hold in $t$-zero divisor graphs for special $t$-norms while giving some additional properties of the zero divisor graph.
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On zero divisor graph of unique product monoid rings over Noetherian reversible ring [PDF]
Categories and General Algebraic Structures with Applications, 2016 Let $R$ be an associative ring with identity and $Z^*(R)$ be its set of non-zero zero divisors.ย The zero-divisor graph of $R$, denoted by $Gamma(R)$, is the graph whose vertices are the non-zeroย zero-divisors ofย $R$, and two distinct vertices $r$ and $
Ebrahim Hashemi +2 more
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The Szeged Index and Padmakar-Ivan Index on the Zero-Divisor Graph of a Commutative Ring
Contemporary Mathematics and Applications (ConMathA)The zero-divisor graph of a commutative ring is a graph where the vertices represent the zero-divisors of the ring, and two distinct vertices are connected if their product equals zero.
Jinan Ambar +2 more
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Decomposition of Neutrosophic Zero-divisor graph [PDF]
Neutrosophic Sets and SystemsEvaluating student performance in university English translation courses is a complex process that requires a comprehensive assessment of multiple factors.
Balakrishnan A +3 more
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Ain Shams Engineering JournalThis paper investigates the outer multiset dimension (OMSD) of compressed zero-divisor graphs (CZDGs) associated with finite commutative rings (CRs). For a given ring A, the classical zero-divisor graph (ZDG) is refined by compressing its nodes based on ...
Amina Riaz +3 more
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Randiฤ spectrum of the weakly zero-divisor graph of the ring โคn
AKCE International Journal of Graphs and CombinatoricsIn this article, we find the Randiฤ spectrum of the weakly zero-divisor graph of a finite commutative ring [Formula: see text] with identity [Formula: see text], denoted as [Formula: see text], where [Formula: see text] is taken as the ring of integers ...
Nadeem Ur Rehman +3 more
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Generalized zero-divisor graph of โ-rings
Asian-European Journal of MathematicsA โ-ring [Formula: see text] is a ring with an involution โ. Let [Formula: see text] denote the set of all nonzero zero-divisors of [Formula: see text]. We associate a simple (undirected) graph [Formula: see text] with vertex set [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent in [Formula: see text]
Anita Lande, Anil Khairnar
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ุฌูุฉ ุจุบุฏุงุฏ ููุนููู
For a commutative ring, a cross monic zero divisor graph is discussed, whose vertices are nonzero zero divisors of the commutative ring, then the two vertices x and y are adjacent if and only if xy = 0.
Sarathy Raja, Ravi Sankar Jeyaraj
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