Results 101 to 110 of about 7,874 (214)

The Wiener index and the Wiener Complexity of the zero-divisor graph of a ring [PDF]

, 2023
We calculate the Wiener index of the zero-divisor graph of a finite semisimple ring. We also calculate the Wiener complexity of the zero-divisor graph of a finite simple ring and find an upper bound for the Wiener complexity in the semisimple ...
Dolžan, David
core  

Graph-theoretic characterization of rings: Outer multiset dimension of compressed zero-divisor graphs

Ain Shams Engineering Journal
This paper investigates the outer multiset dimension (OMSD) of compressed zero-divisor graphs (CZDGs) associated with finite commutative rings (CRs). For a given ring A, the classical zero-divisor graph (ZDG) is refined by compressing its nodes based on ...
Amina Riaz, Hafiz Muhammad Afzal Siddiqui, Muhammad Bilal Riaz, Nasir Ali   +3 more
doaj   +1 more source

Planar Zero-Divisor Graphs

, 2006
Associated to every nonzero commutative ring with identity is a graph whose vertices are the nonzero zero-divisors, and such that two distinct vertices x and y are adjacent if and only if xy = 0.
Chapman, Jeremy M.
core  

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   +1 more source

Graph Operations on Zero-Divisor Graph of Posets

, 2018
We know that some large graphs can be constructed from some smaller graphs by using graphs operations. Many properties of such large graphs are closely related to those of the corresponding smaller ones.
N. Hosseinzadeh (5758513)
core   +1 more source

Generalized zero-divisor graph of ∗-rings

Asian-European Journal of Mathematics
A ∗-ring [Formula: see text] is a ring with an involution ∗. Let [Formula: see text] denote the set of all nonzero zero-divisors of [Formula: see text]. We associate a simple (undirected) graph [Formula: see text] with vertex set [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent in [Formula: see text]
Anita Lande, Anil Khairnar
openaire   +2 more sources

On spectrum of the zero-divisor graph of matrix ring

, 2023
For a ring $R$, the zero-divisor graph is a simple graph $\Gamma(R)$ whose vertex set is the set of all non-zero zero-divisors in a ring $R$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy=0$ or $yx=0$ in $R$.
Lande, Anita, Masalkar, Krishnat, Kadam, Lata, Khairnar, Anil   +3 more
core  

The diameter of a zero divisor graph

, 2006
Let R be a commutative ring and let Z(R)∗ be its set of nonzero zero divisors. The set Z(R)∗ makes up the vertices of the corresponding zero divisor graph, Γ(R), with two distinct vertices forming an edge if the product of the two elements is zero.
Lucas, Thomas G.
core   +1 more source

Graphs from matrices - a survey

AKCE International Journal of Graphs and Combinatorics
Let R be a commutative ring with identity. For a positive integer [Formula: see text] let [Formula: see text] be the set of all n × n matrices over R and [Formula: see text] be the set of all non-zero matrices of [Formula: see text] The zero-divisor ...
T. Tamizh Chelvam
doaj   +1 more source

Zero-divisor graphs of reduced Rickart *-rings

Discussiones Mathematicae - General Algebra and Applications, 2017
For a ring A with an involution *, the zero-divisor graph of A, Γ*(A), is the graph whose vertices are the nonzero left zero-divisors in A such that distinct vertices x and y are adjacent if and only if xy* = 0.
Patil A.A., Waphare B.N.
doaj   +1 more source