Results 61 to 70 of about 1,637,051 (209)

The Zero-Divisor Graph of a Commutative Ring

Journal of Algebra, 1999
The authors study properties of the graph \(\Gamma(R)\) of a commuting ring \(R\) (with \(1\)) defined on the set of nonzero zero-divisors with adjacency relation \((x,y)\in E\) if \(xy= 0\) noting that the class of such graphs is strongly restricted by the (commutative) ring properties of \(R\).
Anderson, David F., Livingston, Philip S.   +1 more
openaire   +1 more source

On the additive image of zeroth persistent homology

Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.
Abstract For a category X$X$ and a finite field F$F$, we study the additive image of the functor H0(−;F)∗:rep(X,Top)→rep(X,VectF)$\operatorname{H}_0(-;F)_* \colon \operatorname{rep}(X, \mathbf {Top}) \rightarrow \operatorname{rep}(X, \mathbf {Vect}_F)$, or equivalently, of the free functor rep(X,Set)→rep(X,VectF)$\operatorname{rep}(X, \mathbf {Set ...
Ulrich Bauer, Magnus B. Botnan, Steffen Oppermann, Johan Steen   +3 more
wiley   +1 more source

THE ZERO DIVISOR IDEAL GRAPH OF THE RING ZN [PDF]

, 2020
In this paper we introduce the notion of Maxideal and Minideal zero divisor graphs of the maximal and minimal ideals of the ring Zn. We defined the Maxideal and Minideal zero divisor graphs of the ring Zn for any n, to be the zero divisor graph of ...
Nazar H Shuker, Payman A Rashed
core  

Computing Wiener and Hyper-Wiener Indices of Zero-Divisor Graph of ℤℊ3×ℤI1I2

Journal of Function Spaces, 2022
Let S=ℤℊ3×ℤI1I2 be a commutative ring where ℊ,I1 and I2 are positive prime integers with I1≠I2. The zero-divisor graph assigned to S is an undirected graph, denoted as YS with vertex set V(Y(S)) consisting of all Zero-divisor of the ring S and for any c,
Yonghong Liu, Abdul Rauf, null AdnanAslam, Saira Ishaq, Abudulai Issa   +4 more
doaj   +1 more source

A tropical version of Martens' theorem for metric graphs

Bulletin of the London Mathematical Society, Volume 58, Issue 10, October 2026.
Abstract We study the conjecture stated by Jensen and Len on a tropical version on Martens' theorem via the Brill–Noether rank of a tropical curve. We recall Coppens' counterexample of Martens‐special chain of cycles, and we generalize the construction defining another class of graphs, Martens‐special trees of cycles, for which the conjecture does not ...
Giusi Capobianco, Angelina Zheng
wiley   +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

On the maximum likelihood degree of Gaussian graphical models

Bulletin of the London Mathematical Society, Volume 58, Issue 10, October 2026.
Abstract In this paper we revisit the likelihood geometry of Gaussian graphical models. We give a detailed proof that the ML‐degree behaves monotonically on induced subgraphs. Furthermore, we complete a missing argument that the ML‐degree of the nth$n{\rm th}$ cycle is larger than 1 for any n⩾4$n\geqslant 4$, therefore completing the characterization ...
Carlos Améndola, Rodica Andreea Dinu, Mateusz Michałek, Martin Vodička   +3 more
wiley   +1 more source

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

bk$b^k$‐Algebroids and the variety of foliation jets

Journal of the London Mathematical Society, Volume 114, Issue 4, October 2026.
Abstract We introduce and classify singular foliations of bk+1$b^{k+1}$‐type, which formalize the properties of vector fields that are tangent to a submanifold W⊂M$W \subset M$ to order k$k$. When W$W$ is a hypersurface, these structures are Lie algebroids generalizing the bk+1$b^{k+1}$‐tangent bundles introduced by Scott.
Francis Bischoff, Álvaro del Pino, Aldo Witte   +2 more
wiley   +1 more source

Algebraic Structure Graphs over the Commutative Ring ${\mathbb{Z}}_m$: Exploring Topological Indices and Entropies Using $\mathbb{M}$-Polynomials

Mathematics, 2023
The field of mathematics that studies the relationship between algebraic structures and graphs is known as algebraic graph theory. It incorporates concepts from graph theory, which examines the characteristics and topology of graphs, with those from ...
Amal S. Alali, Shahbaz Ali, Noor Hassan, Ali M. Mahnashi, Yilun Shang, Abdullah Assiry   +5 more
doaj   +1 more source