Results 11 to 20 of about 22,120 (235)

The Zero-Divisor Graph of a Commutative Ring☆

Journal of Algebra, 1999
For each commutative ring R we associate a (simple) graph Γ(R). We investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of Γ(R).
David F. Anderson, Philip S. Livingston
semanticscholar   +3 more sources

A graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs [PDF]

Heliyon
This article investigates the concept of dominant metric dimensions in zero divisor graphs (ZD-graphs) associated with rings. Consider a finite commutative ring with unity, denoted as R, where nonzero elements x and y are identified as zero divisors if ...
Nasir Ali, Hafiz Muhammad Afzal Siddiqui, Muhammad Bilal Riaz, Muhammad Imran Qureshi, Ali Akgül   +4 more
doaj   +2 more sources

Topological Indices of Total Graph and Zero Divisor Graph of Commutative Ring: A Polynomial Approach

Complexity, 2023
The algebraic polynomial plays a significant role in mathematical chemistry to compute the exact expressions of distance-based, degree-distance-based, and degree-based topological indices.
Sourav Mondal, Muhammad Imran, Nilanjan De, Anita Pal   +3 more
doaj   +2 more sources

On directed zero-divisor graphs of finite rings

Discrete Mathematics, 2004
For an artinian ring $R$, the directed zero-divisor graph $ (R)$ is connected if and only if there is no proper one-sided identity element in $R$. Sinks and sources are characterized and clarified for finite ring $R$, especially, it is proved that for {\it any} ring $R$, if there exists a source $b$ in $ (R)$ with $b^2=0$, then $|R|=4$ and $R=\{0,a,b,
Tongsuo Wu
openalex   +5 more sources

Sub-semigroups determined by the zero-divisor graph

Discrete Mathematics, 2005
In this paper we study sub-semigroups of a zero-divisor semigroup $S$ determined by properties of the zero-divisor graph $ (S)$. We use these sub-semigroups to study the correspondence between zero- divisor semigroups and zero-divisor graphs. We study properties of sub- semigroups of Boolean semigroups via the zero-divisor graph. As an application, we
Tongsuo Wu, Dancheng Lu
openalex   +5 more sources

The zero-divisor graphs of semirings

, 2010
17 pages, Section 4 has been added to ...
David Dolžan, Polona Oblak
openalex   +4 more sources

Randić spectrum of the weakly zero-divisor graph of the ring ℤn

AKCE International Journal of Graphs and Combinatorics
In this article, we find the Randić spectrum of the weakly zero-divisor graph of a finite commutative ring [Formula: see text] with identity [Formula: see text], denoted as [Formula: see text], where [Formula: see text] is taken as the ring of integers ...
Nadeem Ur Rehman, Nazim, Ahmad M. Alghamdi, Eman S. Almotairi   +3 more
doaj   +2 more sources

Ring Classification of Ideal-Based Zero Divisor Graph with Vertices 9

Al-Kitab Journal for Pure Sciences
Let R be a finite commutative ring with a non-zero unit, and L be an ideal of R. focuses on expanding the notation of the Zero Divisor Graph to create what is known as the Ideal-Based Zero Divisor Graph. The main goal is to classify rings using the ideal-
Husam Q. Mohammad, Sahbaa A. Younus, Wafa Y. Yahya   +2 more
doaj   +2 more sources

The Szeged Index and Padmakar-Ivan Index on the Zero-Divisor Graph of a Commutative Ring

Contemporary Mathematics and Applications (ConMathA)
The zero-divisor graph of a commutative ring is a graph where the vertices represent the zero-divisors of the ring, and two distinct vertices are connected if their product equals zero.
Jinan Ambar, I Gede Adhitya Wisnu Wardhana, Abdurahim   +2 more
doaj   +2 more sources

A note on the Independent domination polynomial of zero divisor graph of rings

arXiv.org
In this note we consider the independent domination polynomial problem along with their unimodal and log-concave properties which were earlier studied by G\"ursoy, \"Ulker and G\"ursoy (Soft Comp. 2022). We show that the independent domination polynomial
Bilal Ahmad Rather
openalex   +3 more sources