Results 111 to 120 of about 1,233,365 (217)

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  

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 Comparison of Zero Divisor Graphs [PDF]

, 2009
A zero divisor graph of a ring R is a visual representation of the zero divisors and their relationships in R. (If a and b are non-zero elements in R such that ab = 0, then a and b are vertices of the graph and connected by an edge.) These graphs have ...
Spiroff, Sandra
core   +1 more source

Zero-divisor graphs of lower dismantlable lattices I

, 2017
In this paper, we study the zero-divisor graphs of a subclass of dismantlable lattices. These graphs are characterized in terms of the non-ancestor graphs of rooted trees.
Avinash Patil, Hossein Y. Pourali, Vinayak Joshi, B. N. Waphare   +3 more
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

On zero-divisor graphs of infinite posets

Soft Computing
AbstractIt is known that the so-called Beck’s conjecture, i.e. the equality of the finite clique and chromatic numbers of a zero-divisor graph, holds for partially ordered sets Halaš and Jukl (Discrete Math 309(13):4584–4589, 2009). In this paper we present a simple direct proof of this fact.
Radomír Halas, Jozef Pócs
openaire   +1 more source

Graceful labeling of zero-divisor graph Γ(ℤp²q) and Γ(ℤp³q)

Electronic Journal of Graph Theory and Applications
Some papers have already provided graceful labeling for some types of zero-divisor graphs. We reviewed the graceful labeling results of Γ(ℤ25), Γ(ℤ8), and Γ(ℤ27), then use those results to label zero-divisors graphs Γ(ℤ25q), Γ(ℤ8q), and Γ(ℤ27q).The ...
Christian Constantine, Erma Suwastika
doaj   +1 more source

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

An exploration of ideal-divisor graphs

, 2014
Zero-divisor graphs have given some interesting insights into the behavior of commutative rings. Redmond introduced a generalization of the zero-divisor graph called an ideal-divisor graph.
Williams, Tristan, Peck, Hailee, Richard, Abigail, Donovan, Rob, Stickles, Joe, Axtell, Michael, Milner, Paul, Bloome, Lane   +7 more
core   +1 more source

Eigenvalues of zero-divisor graphs

V diplomski nalogi spoznamo grafe deliteljev niča. Ti povežejo algebrajske strukture in teorijo grafov na zanimiv in intuitiven način. Tako lahko s študijem enega področja pridemo do uporabnih dognanj na drugem.
Verbič, Jošt
core