Results 31 to 40 of about 1,283,908 (223)
On bipartite zero-divisor graphs
Discrete Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dancheng Lu, Tongsuo Wu
openaire +1 more source
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
openaire +2 more sources
On a New Extension of the Zero-Divisor Graph [PDF]
Algebra Colloquium, 2020 In this paper, we introduce a new graph whose vertices are the non-zero zero-divisors of a commutative ring R, and for distincts elements x and y in the set Z(R)* of the non-zero zero-divisors of R, x and y are adjacent if and only if xy = 0 or x + y ∈ Z(R).
Cherrabi, A. +3 more
openaire +2 more sources
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
doaj +1 more source
Frequency Assignment Model of Zero Divisor Graph [PDF]
Journal of Applied Mathematics, 2021 Given a frequency assignment network model is a zero divisor graph Γ = V , E
R. Radha, N. Mohamed Rilwan
openaire +3 more sources
Cut-structures in zero-divisor graphs of commutative rings
, 2016 Zero-divisor graphs, and more recently, compressed zero-divisor graphs are well represented in the commutative ring literature. In this work, we consider various cut structures, sets of edges or vertices whose removal disconnects the graph, in both ...
Axtell, Mike +2 more
core +1 more source
Group Action on the Set of Nonunits in Rings
Journal of Mathematics, 2023 Let R be a ring, G be the group of all units of R, and X=R−G∪0. In this paper, we investigate avxx∈X=oxx∈X for a ring R, where avx is the set of all vertices of the zero-divisor graph of R adjacent to x.
Eman S. Almotairi +2 more
doaj +1 more source
ZERO-DIVISOR GRAPHS OF FINITE COMMUTATIVE RINGS: A SURVEY [PDF]
Surveys in Mathematics and its Applications, 2020 This article gives a comprehensive survey on zero-divisor graphs of finite commutative rings. We investigate the results on structural properties of these graphs.
Pradeep Singh, Vijay Kumar Bhat
doaj
On Global Offensive Alliance in Zero-Divisor Graphs
Mathematics, 2022 Let Γ(V,E) be a simple connected graph with more than one vertex, without loops or multiple edges. A nonempty subset S⊆V is a global offensive alliance if every vertex v∈V−S satisfies that δS(v)≥δS¯(v)+1.
Raúl Juárez Morales +3 more
doaj +1 more source
Boxicity of zero divisor graphs
Discrete Applied MathematicsA $d$-dimensional box is the cartesian product $R_i\times\cdots\times R_d$ where each $R_i$ is a closed interval on the real line. The boxicity of a graph, denoted as $box(G)$, is the minimum integer $d\geq 0$ such that $G$ is the intersection graph of a collection of $d$-dimensional boxes.
L. Sunil Chandran, Suraj Kumar Sahoo
openaire +3 more sources