Results 111 to 120 of about 1,637,051 (209)

Cut-sets and Cut-vertices in the Zero-Divisor Graph of ∏Zni [PDF]

, 2017
We examine minimal sets of vertices which, when removed from a zero-divisor graph, separate the graph into disconnected subgraphs.
Ewing, Caroline, Weber, Darrin, Huhn, Michael, Plaut, Chelsea, Coté, Benjamin   +4 more
core   +1 more source

On the connectedness of the complement of the zero-divisor graph of a poset

, 2019
In this paper, connectedness is completely characterized for the complements of the zero-divisor graphs of partially ordered sets. These results are applied to annihilating ideal graphs and intersection graphs of submodules, generalizing some of the work
Joshi, Vinayak, LaGrange, John, Devhare, Sarika   +2 more
core  

Laplacian Energy and Eccentricity Based Energy for Cross Monic Zero Divisor Graph Associated With Commutative Rings

مجلة بغداد للعلوم
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
doaj   +1 more source

On zero-divisor graphs of infinite posets

Soft Computing
AbstractIt is known that the so-called Beck’s conjecture, i.e. the equality of the finite clique and chromatic numbers of a zero-divisor graph, holds for partially ordered sets Halaš and Jukl (Discrete Math 309(13):4584–4589, 2009). In this paper we present a simple direct proof of this fact.
Radomír Halas, Jozef Pócs
openaire   +1 more source

Graphs from matrices - a survey

AKCE International Journal of Graphs and Combinatorics
Let R be a commutative ring with identity. For a positive integer [Formula: see text] let [Formula: see text] be the set of all n × n matrices over R and [Formula: see text] be the set of all non-zero matrices of [Formula: see text] The zero-divisor ...
T. Tamizh Chelvam
doaj   +1 more source

Properties of ideal-based zero-divisor graphs of commutative rings [PDF]

, 2014
Let R be a commutative ring with nonzero identity and I an ideal of R. The focus of this research is on a generalization of the zero-divisor graph called the ideal-based zero-divisor graph for commutative rings with nonzero identity.
Jesse Gerald Smith, Jr., Smith, Jesse Gerald, Jr.   +1 more
core  

CLASSIFICATION OF RINGS WITH GENUS ONE ZERO-DIVISOR GRAPHS

, 2008
. This paper investigates properties of the zero-divisor graph of a commutative ring and its genus. In particular, we determine all isomorphism classes of finite commutative rings with identity whose zero-divisor graph has genus 1 ...
Cameron Wickham, Wickham, Cameron
core   +1 more source

Zero divisor graphs of skew Hurwitz series rings [PDF]

, 2018
For a ring endomorphism $\alpha$, we investigate theinterplay between the ring-theoretical properties of the skewHurwitz series ring $(HR, \alpha )$ and the graph-theoreticalproperties of its zero-divisor graph $\overline{\Gamma}((HR, \alpha ...
Daneshmand, Hossein, Paykan, Kamal
core   +1 more source

Divisor graph of the complement of Γ(R)

, 2019
Let [Formula: see text] be the complement of the zero-divisor graph of a finite commutative ring [Formula: see text]. In this paper, we provide the answer of the question (ii) raised by Osba and Alkam in [11] and prove that [Formula: see text] is a ...
Ravindra Kumar, Om Prakash
core   +1 more source

Grafo divisor de zero de um anel comutativo [PDF]

, 2011
Let R be a commutative ring with identity and let D(R) ∗ be its set of nonzero zerodivisors. The zero-divisor graph of R, denoted bySejam R um anel comutativo com identidade e D(R) ∗ seu conjunto de divisores de zero não nulos.
Claudia Juliana Fanelli Gonçalves
core