Results 31 to 40 of about 1,283,848 (178)

Commutative rings with ideal based zero divisor graph of orders 12,13 and 14 [PDF]

Al-Rafidain Journal of Computer Sciences and Mathematics
An recent years, several studies have emerged on the graphs for commutative rings. Researchers have investigated ideal based zero-divisor graphs linked to commutative rings, delving into the characteristics of these graphs.
Raad Shukur, Husam Mohammad
doaj   +1 more source

On determining number and metric dimension of zero-divisor graphs [PDF]

, 2023
In this article, explicit formulas for finding the determining number and the metric dimension of the zero-divisor graph of Z_n and non-Boolean semisimple rings are given.
K, Muhammed Sabeel, Paramasivam, Krishnan   +1 more
core   +1 more source

Five Point Zero Divisor Graphs [PDF]

, 2010
We study the zero divisor graphs, determined by equivalence classes of zero divisors of a ring R. with exactly five vertices. In particular, we determine which graphs with exactly five vertices can be realized as the zero divisor graph of a ring.
Levidiotis, Florida Victoria
core   +1 more source

Directed zero-divisor graph and skew power series rings [PDF]

Transactions on Combinatorics, 2018
‎Let $R$ be an associative ring with identity and $Z^{\ast}(R)$ be its set of non-zero zero-divisors‎. ‎Zero-divisor graphs of rings are well represented in the literature of commutative and non-commutative rings‎. ‎The directed zero-divisor graph of $R$‎
Ebrahim Hashemi, Marzieh Yazdanfar, Abdollah Alhevaz   +2 more
doaj   +1 more source

Cut-structures in zero-divisor graphs of commutative rings

, 2016
Zero-divisor graphs, and more recently, compressed zero-divisor graphs are well represented in the commutative ring literature. In this work, we consider various cut structures, sets of edges or vertices whose removal disconnects the graph, in both ...
Axtell, Mike, Baeth, Nicholas R., Stickles, Joe   +2 more
core   +1 more source

Group Action on the Set of Nonunits in Rings

Journal of Mathematics, 2023
Let R be a ring, G be the group of all units of R, and X=R−G∪0. In this paper, we investigate avxx∈X=oxx∈X for a ring R, where avx is the set of all vertices of the zero-divisor graph of R adjacent to x.
Eman S. Almotairi, M. Imran Bhat, Ahmad M. Alghamdi   +2 more
doaj   +1 more source

ZERO-DIVISOR GRAPHS OF FINITE COMMUTATIVE RINGS: A SURVEY [PDF]

Surveys in Mathematics and its Applications, 2020
This article gives a comprehensive survey on zero-divisor graphs of finite commutative rings. We investigate the results on structural properties of these graphs.
Pradeep Singh, Vijay Kumar Bhat
doaj  

On Global Offensive Alliance in Zero-Divisor Graphs

Mathematics, 2022
Let Γ(V,E) be a simple connected graph with more than one vertex, without loops or multiple edges. A nonempty subset S⊆V is a global offensive alliance if every vertex v∈V−S satisfies that δS(v)≥δS¯(v)+1.
Raúl Juárez Morales, Gerardo Reyna Hernández, Omar Rosario Cayetano, Jesús Romero Valencia   +3 more
doaj   +1 more source

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