Results 11 to 20 of about 1,283,908 (223)

Zero-divisor graphs and zero-divisor functors [PDF]

Journal of Algebra and Its Applications, 2023
Inspired by a very recent work of A. Đurić, S. Jevđenić and N. Stopar, we introduce a new definition of zero-divisor graphs attached to rings that includes all of the classical definitions already known in the literature. We provide an interpretation of such graphs by means of a functor that we call zero-divisor functor and which is associated with a ...
Enrico Sbarra, Maurizio Zanardo
openaire   +4 more sources

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, Stickles, Joe, Trampbachls, Wallace   +2 more
openaire   +4 more sources

Component graphs of vector spaces and zero-divisor graphs of ordered sets [PDF]

AKCE International Journal of Graphs and Combinatorics
In 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, Peter J. Cameron, Vinayak Joshi   +2 more
doaj   +2 more sources

Dynamic multi‐objective optimisation of complex networks based on evolutionary computation

IET Networks, EarlyView., 2022
Abstract As the problems concerning the number of information to be optimised is increasing, the optimisation level is getting higher, the target information is more diversified, and the algorithms are becoming more complex; the traditional algorithms such as particle swarm and differential evolution are far from being able to deal with this situation ...
Linfeng Huang
wiley   +1 more source

On distance Laplacian spectrum of zero divisor graphs of the ring $\mathbb{Z}_{n}$

Karpatsʹkì Matematičnì Publìkacìï, 2021
For a finite commutative ring $\mathbb{Z}_{n}$ with identity $1\neq 0$, the zero divisor graph $\Gamma(\mathbb{Z}_{n})$ is a simple connected graph having vertex set as the set of non-zero zero divisors, where two vertices $x$ and $y$ are adjacent if and
S. Pirzada, B.A. Rather, T.A. Chishti
doaj   +1 more source

GENERALIZATIONS OF THE ZERO-DIVISOR GRAPH

International Electronic Journal of Algebra, 2020
Summary: Let \(R\) be a commutative ring with \(1\neq 0\) and \(Z(R)\) its set of zerodivisors. The zero-divisor graph of \(R\) is the (simple) graph \(\Gamma \)(R) with vertices \(Z(R) \backslash \{0\}\), and distinct vertices \(x\)and \(y\) are adjacent if and only if \(xy= 0\).
ANDERSON, David F., MCCLURKİN, Grace
openaire   +4 more sources

Classification of Genus Three Zero-Divisor Graphs

, 2023
In this paper, we consider the problem of classifying commutative rings according to the genus number of its associating zero-divisor graphs. The zero-divisor graph of R, where R is a commutative ring with nonzero identity, denoted by Γ(R), is the ...
Turki Alsuraiheed, Karuppiah Mano, Thangaraj Asir   +2 more
core   +1 more source

THE ZERO-DIVISOR GRAPHS OF RINGS AND SEMIRINGS [PDF]

International Journal of Algebra and Computation, 2012
In this paper we study zero-divisor graphs of rings and semirings. We show that all zero-divisor graphs of (possibly noncommutative) semirings are connected and have diameter less than or equal to 3. We characterize all acyclic zero-divisor graphs of semirings and prove that in the case zero-divisor graphs are cyclic, their girths are less than or ...
David Dolzan, Polona Oblak
openaire   +2 more sources

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
doaj   +1 more source

Exploring the properties of the zero-divisor graph of direct product of $\ast$-rings [PDF]

Journal of Mahani Mathematical Research
In this paper, we delve into the study of zero-divisor graphs in rings equipped with an involution. Specifically, we focus on abelian Rickart $\ast$-rings.
Mohd Nazim, Nadeem Ur Rehman, Shabir Ahmad Mir   +2 more
doaj   +1 more source