Results 41 to 50 of about 1,283,908 (223)

Zero-divisor Graphs of Localizations and Modular Rings [PDF]

, 2017
In this paper, we examine the algebraic properties of localizations of commutative rings and how localizations affect the zero-divisor graphs structure of modular rings.
Cuchta, Thomas, Young, William, Lokken, Kathryn A.   +2 more
core   +1 more source

The Zero Divisor Graph of the Ring Z_(2^2 p)

ARO-The Scientific Journal of Koya University, 2016
In this paper, we consider the crossing number and the chromatic number of the zero divisor graph Γ(Z_(2^2 p)) to show that this type of zero divisor graphs is bipartite graph, and the smallest cycle in Γ(Z_(2^2 p)) is of length four this implies that ...
Nazar H. Shuker, Payman A. Rashed
doaj   +1 more source

Zero-divisor graphs of idealizations

, 2006
We consider zero-divisor graphs of idealizations of commutative rings. Specifically, we look at the preservation, or lack thereof, of the diameter and girth of the zero-divisor graph of a ring when extending to idealizations of the ...
Stickles, Joe, Axtell, Michael
core   +1 more source

Line Graphs of Monogenic Semigroup Graphs

Journal of Mathematics, 2021
The concept of monogenic semigroup graphs ΓSM is firstly introduced by Das et al. (2013) based on zero divisor graphs. In this study, we mainly discuss the some graph properties over the line graph LΓSM of ΓSM.
Nihat Akgunes, Yasar Nacaroglu, Sedat Pak   +2 more
doaj   +1 more source

A class of zero divisor rings in which every graph is precisely the union of a complete graph and a complete bipartite graph

Open Mathematics, 2015
Recently, an interest is developed in estimating genus of the zero-divisor graph of a ring. In this note we investigate genera of graphs of a class of zero-divisor rings (a ring in which every element is a zero divisor).
Nauman Syed Khalid, Shafee Basmah H.
doaj   +1 more source

The Zero Divisor Graphs of a finite Certain Rings [PDF]

المجلة العراقية للعلوم الاحصائية, 2013
For each commutative ring we associate a ...
Nazar H. Shuker, Husam Q. Mohammad
doaj   +1 more source

COMPLEMENT OF THE ZERO DIVISOR GRAPH OF A LATTICE [PDF]

Bulletin of the Australian Mathematical Society, 2013
AbstractIn this paper, we determine when $\mathop{({\Gamma }_{I} (L))}\nolimits ^{c} $, the complement of the zero divisor graph ${\Gamma }_{I} (L)$ with respect to a semiprime ideal $I$ of a lattice $L$, is connected and also determine its diameter, radius, centre and girth. Further, a form of Beck’s conjecture is proved for ${\Gamma }_{I} (L)$ when $\
Joshi, Vinayak, Khiste, Anagha
openaire   +1 more source

Catalan Bounds for Symmetric Strength‐Two Orthogonal Arrays

Journal of Combinatorial Designs, EarlyView.
ABSTRACT A Hamming shell construction is a two‐level array obtained by taking every binary vector of a given Hamming weight a prescribed number of times, for each weight in turn. Such arrays are invariant under all permutations of the factors, and they are strength‐two orthogonal arrays exactly when the multiplicities satisfy three linear constraints ...
Ruwan C. Karunanayaka
wiley   +1 more source

Adjacency spectra and Laplacian integrality of zero divisor graphs over some rings

Kuwait Journal of Science
Let 𝑅 be a commutative ring and let 𝑍∗ (𝑅) denote the set of non-zero zero divisors of 𝑅. The zero divisor graph 𝛤(𝑅) is defined as the simple graph with vertex set 𝑍∗ (𝑅), where two distinct vertices 𝑥, 𝑦 ∈ 𝑍∗ (𝑅) are adjacent if and only if 𝑥𝑦 = 0.
Bilal Ahmad Rather, Parvez Ali, M. Imran, A. Kothepeda   +3 more
doaj   +1 more source

A generalization of zero-divisor graphs

CoRR, 2019
One reference added.
openaire   +3 more sources