Results 31 to 40 of about 600 (179)
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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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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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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Induced subgraphs of zero-divisor graphs
Discrete Mathematics, 2023 The zero-divisor graph of a finite commutative ring with unity is the graph whose vertex set is the set of zero-divisors in the ring, with $a$ and $b$ adjacent if $ab=0$. We show that the class of zero-divisor graphs is universal, in the sense that every finite graph is isomorphic to an induced subgraph of a zero-divisor graph.
G. Arunkumar +3 more
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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
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On Reduced Zero-Divisor Graphs of Posets [PDF]
Journal of Discrete Mathematics, 2015 We study some properties of a graph which is constructed from the equivalence classes of nonzero zero-divisors determined by the annihilator ideals of a poset. In particular, we demonstrate how this graph helps in identifying the annihilator prime ideals of a poset that satisfies the ascending chain condition for its proper annihilator ideals.
Ashish Kumar Das, Deiborlang Nongsiang
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Distances in zero-divisor and total graphs from commutative rings–A survey
AKCE International Journal of Graphs and Combinatorics, 2016 There are so many ways to construct graphs from algebraic structures. Most popular constructions are Cayley graphs, commuting graphs and non-commuting graphs from finite groups and zero-divisor graphs and total graphs from commutative rings.
T. Tamizh Chelvam, T. Asir
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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
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Component graphs of vector spaces and zero-divisor graphs of ordered sets
AKCE International Journal of Graphs and CombinatoricsIn this paper, nonzero component graphs and nonzero component union graphs of finite-dimensional vector spaces are studied using the zero-divisor graph of a specially constructed 0–1-distributive lattice and the zero-divisor graph of rings.
Nilesh Khandekar +2 more
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