Results 121 to 130 of about 1,283,908 (223)

Energy of zero-divisor graphs via distance-based fuzzy adjacency matrices

In this paper, we investigate the energy of zero-divisor graphs of finite commutative rings with unity using the distance-based fuzzy adjacency matrix. In view of this, first we characterize the rings whose zero-divisor graphs have energy zero and then ...
Rakesh Kumar, R.K. Bairwa, Pranjali
core   +1 more source

Colorings of Zero-Divisor Graphs of Commutative Rings [PDF]

, 2015
We will focus on Beck?s conjecture that the chromatic number of a zero-divisor graph of a ring R is equal to the clique number of the ring R. We begin by calculating the chromatic number of the zero-divisor graphs for some finite rings and characterizing
Ramos, Rebecca Elizabeth
core  

Construction of Graphs and Zero-Divisor Graphs by Degree-Joint Operations of Graphs

International Journal of Mathematics and Mathematical Sciences
The new construction of graphs obtained by degree-joint operations between maximum-degree and minimum-degree of some types of graphs with different vertex and edge sets denoted by Gδ,GΔ respectively, joins vertices of maximum (minimum) degree in one ...
Mohammed N. Authman, Payman A. Rashed, Husam Q. Mohammad   +2 more
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  

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

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

Local Rings with Genus Two Zero Divisor Graph

, 2010
To each commutative ring R we can associate a graph, the zero divisor graph of R, whose vertices are the zero divisors of R, and such that two vertices are adjacent if their product is zero.
Bloomfield, Nathan, Nathan Bloomfield, Cameron Wickham, Wickham, Cameron   +3 more
core   +1 more source

A Combinatorial Analysis of Zero-Divisor Graphs on Certain Polynomial Rings

, 2013
The colouring of zero-divisor graphs on certain quotients of polynomial rings can be effectively studied by virtue of a natural correspondence between the algebraic and the combinatorial structure.
VIETRI, Andrea
core   +1 more source

Harary and hyper-Wiener indices of some graph operations

Journal of Inequalities and Applications
In this paper, we obtain the Harary index and the hyper-Wiener index of the H-generalized join of graphs and the generalized corona product of graphs. As a consequence, we deduce some of the results in (Das et al. in J. Inequal. Appl. 2013:339, 2013) and
S. Balamoorthy, T. Kavaskar, K. Vinothkumar   +2 more
doaj   +1 more source

The Congruence-Based Zero-Divisor Graph [PDF]

, 2015
Let R be a commutative ring with nonzero identity and ~ a multiplicative congruence relation on R. Then, R/~ is a semigroup with multiplication [x][y] = [xy], where [x] is the congruence class of an element x of R.
Lewis, Elizabeth Fowler
core