Results 11 to 20 of about 1,637,051 (209)

Non Deterministic Zero Divisor Graph [PDF]

Ratio Mathematica, 2023
A non-deterministic zero divisor graph refers to an element in a ring or algebraic structure that can multiply with another element to give zero, but the specific outcome of the multiplication is not uniquely determined.
Shakila Banu, Naveena Selvaraj
doaj   +2 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

Zero Divisor Graph of Quotient Ring [PDF]

Cauchy: Jurnal Matematika Murni dan Aplikasi
Recently, a lot of research has been carried out regarding graphs built from algebraic structures, including ring structures. One important example of a graph constructed from a ring is the zero divisor graph.
Ayunda Faizatul Musyarrofah, Vira Hari Krisnawati, Noor Hidayat   +2 more
doaj   +2 more sources

Harary index of the zero divisor graph of upper triangular matrices [PDF]

Scientific Reports
The Harary Index is an important topological parameter for examining the structure of a graph. This work presents a quantitative analysis of the structural features of zero-divisor graph using the Harary Index.
Omaima Alshanqiti, Sahil Sharma, Vijay Kumar Bhat   +2 more
doaj   +2 more sources

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   +2 more sources

On Normalized Laplacian Spectra of the Weakly Zero-Divisor Graph of the Ring ℤ_n

Mathematics, 2023
For a finite commutative ring R with identity 1≠0, the weakly zero-divisor graph of R denoted as WΓ(R) is a simple undirected graph having vertex set as a set of non-zero zero-divisors of R and two distinct vertices a and b are adjacent if and only if ...
Nazim, Nadeem Ur Rehman, Ahmad Alghamdi
doaj   +2 more sources

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

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   +2 more sources

Note on Ideal Based Zero-Divisor Graph of a Commutative Ring [PDF]

Discussiones Mathematicae - General Algebra and Applications, 2017
In this paper, we consider the ideal based zero divisor graph ΓI(R) of a commutative ring R. We discuss some graph theoretical properties of ΓI(R) in relation with zero divisor graph.
Mallika A., Kala R., Selvakumar K.
doaj   +3 more sources

A note on the zero divisor graph of a lattice [PDF]

Transactions on Combinatorics, 2014
Let $L$ be a lattice with the least element $0$. An element $xin L$ is a zero divisor if $xwedge y=0$ for some $yin L^*=Lsetminus left{0right}$. The set of all zero divisors is denoted by $Z(L)$.
T. Tamizh Chelvam , S. Nithya
doaj   +1 more source

A Study on the Structure of Ideal-Based Non-Zero Divisor Graphs Associated with Zn [version 1; peer review: 2 approved] [PDF]

F1000Research
Background The study of algebraic structures through graph-theoretic representations provides a powerful visual and combinatorial framework for analyzing ring-theoretic properties. The ideal-based non-zero divisor graph ∅ I ( Z n ) , constructed from the
Ali Abd Aubad, Sameer Kadem
doaj   +2 more sources