Results 111 to 120 of about 1,460,755 (212)

An exploration of ideal-divisor graphs

, 2014
Zero-divisor graphs have given some interesting insights into the behavior of commutative rings. Redmond introduced a generalization of the zero-divisor graph called an ideal-divisor graph.
Williams, Tristan, Peck, Hailee, Richard, Abigail, Donovan, Rob, Stickles, Joe, Axtell, Michael, Milner, Paul, Bloome, Lane   +7 more
core   +1 more source

Generalized zero-divisor graph of ∗-rings

Asian-European Journal of Mathematics
A ∗-ring [Formula: see text] is a ring with an involution ∗. 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
openaire   +2 more sources

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

Graph Operations on Zero-Divisor Graph of Posets

, 2018
We know that some large graphs can be constructed from some smaller graphs by using graphs operations. Many properties of such large graphs are closely related to those of the corresponding smaller ones.
N. Hosseinzadeh (5758513)
core   +1 more source

On spectrum of the zero-divisor graph of matrix ring [PDF]

, 2023
For a ring $R$, the zero-divisor graph is a simple graph $\Gamma(R)$ whose vertex set is the set of all non-zero zero-divisors in a ring $R$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy=0$ or $yx=0$ in $R$.
Lande, Anita, Masalkar, Krishnat, Kadam, Lata, Khairnar, Anil   +3 more
core  

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  

Strong zero-divisor graph of p.q.-Baer $*$-rings [PDF]

In this paper, we study the strong zero-divisor graph of a p.q.-Baer $*$-ring. We determine the condition on a p.q.-Baer $*$-ring (in terms of the smallest central projection in a lattice of central projections of a $*$-ring), so that its strong zero ...
Waphare, B. N., Kumbhar, Nana, Khairnar, Anil   +2 more
core  

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  

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

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