Results 21 to 30 of about 600 (179)
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 ideals and realizable zero-divisor graphs [PDF]
Involve, a Journal of Mathematics, 2009 We seek to classify the sets of zero-divisors that form ideals based on their zero-divisor graphs. We offer full classification of these ideals within finite commutative rings with identity. We also provide various results concerning the realizability of a graph as a zero-divisor graph. 1.
Axtell, Michael +2 more
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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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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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Discrete Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Avinash Patil +2 more
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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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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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