Results 111 to 120 of about 1,283,908 (223)

In The Graph Based on a Given Ideal of a Ring

Zanco Journal of Pure and Applied Sciences, 2019
In this paper we introduce a new kind of graph associated with a commutative ring with identity, and we discover some of its characterizations and properties. Let R be a commutative ring with identity and K be a non-trivial ideal of R.
friad husen abdulqadr
doaj   +1 more source

Zero-divisor Graphs of Localizations and Modular Rings

, 2008
In this paper, we examine the algebraic properties of localizations of commutative rings and how localizations affect the zero-divisor graph’s structure of modular rings.
Young, William, Lokken, Kathryn A., Cuchta, Tom   +2 more
core  

ZERO-DIVISOR GRAPHS OF ÖRE EXTENSION RINGS

, 2011
Let R be an associative ring with two-sided multiplicative identity. In this paper, in the case that R is a commutative α-compatible ring, we compare the diameter (and girth) of the zero-divisor graphs Γ(R) and Γ(R[x;α, δ]).
M. R. KHORSANDI, K. KHASHYARMANESH, M. AFKHAMI   +2 more
core   +1 more source

Construction of Binary Linear Codes from Zero Divisor Graphs

Science and Technology Indonesia
Binary linear codes play an essential role in communication systems by ensuring reliable data transmission. One approach to constructing binary linear codes is through graph theory. In this paper, we study the construction of binary linear codes derived
Vira Hari Krisnawati, Ardi Nur Hidayat, Muhammad Husnul Khuluq   +2 more
doaj   +1 more source

Diameter of Zero Divisor Graphs of Finite Direct Product of Lattices

, 2014
In this paper, we verify the diameter of zero divisor graphs with respect to direct ...
V. V. Joshi, H. Y. Pourali, B. N. Waphare.   +2 more
core   +1 more source

Zero-divisor graphs of direct products of commutative rings

, 2006
We recall several results of zero divisor graphs of commutative rings. We then examine the preservation of diameter and girth of the zero divisor graph of direct products of commutative ...
Warfel, Joseph, Stickles, Joe, Axtell, Michael   +2 more
core  

Eulerian and pancyclic zero-divisor graphs of ordered sets

AKCE International Journal of Graphs and Combinatorics
In this paper, we determine when the zero-divisor graph of a special class of a finite pseudocomplemented poset is Eulerian. Also, we deal with Hamiltonian, vertex pancyclic, and edge pancyclic properties of the complement of a zero-divisor graph of ...
Nilesh Khandekar, Vinayak Joshi
doaj   +1 more source

A Graph-Theoretic Approach to Ring Analysis: Dominant Metric Dimensions in Zero-Divisor Graphs

, 2023
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 ...
Ali, Nasir, Qureshi, Muhammad Imran, Siddiqui, Hafiz Muhammad Afzal   +2 more
core  

On the zero divisor graphs of Galois rings [PDF]

, 2015
Paper presented at the 3rd Strathmore International Mathematics Conference (SIMC 2015), 3 - 7 August 2015, Strathmore University, Nairobi, Kenya.Let R be a Galois ring.
Oduor, Maurice Owino
core   +1 more source

Fault-Tolerant Metric Dimension and Applications: Zero-Divisor Graph of Upper Triangular Matrices

Mathematics
Graph invariants play a crucial role in understanding the structural and combinatorial characteristics of graphs. The fault-tolerant metric dimension, as a significant graph invariant, finds applications in diverse areas such as robust network ...
Latif Abdelmalek Hanna, Maryam M. Alkandari, Vijay Kumar Bhat   +2 more
doaj   +1 more source