Results 21 to 30 of about 17,702 (242)

Wiener index of graphs over rings: a survey

AKCE International Journal of Graphs and Combinatorics, 2022
This article presents a survey of results consisting of the Wiener index of graphs associated with commutative rings. In particular, we focus on zero-divisor graphs, unit graphs, total graphs and prime graphs.
T. Asir, V. Rabikka, A. M. Anto, N. Shunmugapriya   +3 more
doaj   +1 more source

A Zero Divisor Graph Determined by Equivalence Classes of Zero Divisors [PDF]

Communications in Algebra, 2011
We study the zero divisor graph determined by equivalence classes of zero divisors of a commutative Noetherian ring R. We demonstrate how to recover information about R from this structure. In particular, we determine how to identify associated primes from the graph.
Spiroff, Sandra, Wickham, Cameron
openaire   +2 more sources

On distance Laplacian spectrum of zero divisor graphs of the ring $\mathbb{Z}_{n}$

Karpatsʹkì Matematičnì Publìkacìï, 2021
For a finite commutative ring $\mathbb{Z}_{n}$ with identity $1\neq 0$, the zero divisor graph $\Gamma(\mathbb{Z}_{n})$ is a simple connected graph having vertex set as the set of non-zero zero divisors, where two vertices $x$ and $y$ are adjacent if and
S. Pirzada, B.A. Rather, T.A. Chishti
doaj   +1 more source

Zero divisor graphs of semigroups

Journal of Algebra, 2005
Let \(S\) be a commutative semigroup with \(0\). A simple graph \(G\) whose vertices are the nonzero zero divisors of \(S\) with two distinct vertices joined by an edge in case when their product in \(S\) is \(0\) is called the zero divisor graph of \(S\). In the paper some characterizations of graphs to be zero divisor graphs of a semigroup are given.
DeMeyer, Frank, DeMeyer, Lisa
openaire   +2 more sources

Distances in zero-divisor and total graphs from commutative rings–A survey

AKCE International Journal of Graphs and Combinatorics, 2016
There are so many ways to construct graphs from algebraic structures. Most popular constructions are Cayley graphs, commuting graphs and non-commuting graphs from finite groups and zero-divisor graphs and total graphs from commutative rings.
T. Tamizh Chelvam, T. Asir
doaj   +1 more source

Review of: "Zero-Divisor Graphs of ℤ_n, their products and D_n" [PDF]

, 2023
Imran Javaid
  +10 more sources

Exploring the properties of the zero-divisor graph of direct product of $\ast$-rings [PDF]

Journal of Mahani Mathematical Research
In this paper, we delve into the study of zero-divisor graphs in rings equipped with an involution. Specifically, we focus on abelian Rickart $\ast$-rings.
Mohd Nazim, Nadeem Ur Rehman, Shabir Ahmad Mir   +2 more
doaj   +1 more source

Computation of eccentric topological indices of zero-divisor graphs based on their edges

AIMS Mathematics, 2022
The topological index of a graph gives its topological property that remains invariant up to graph automorphism. The topological indices which are based on the eccentricity of a chemical graph are molecular descriptors that remain constant in the whole ...
Ali N. A. Koam, Ali Ahmad , Azeem Haider, Moin A. Ansari   +3 more
doaj   +1 more source

Planar zero-divisor graphs

Journal of Algebra, 2007
The authors answer two questions about zero divisor graphs posed by \textit{S.~Akbari, H. R.~Maimani} and \textit{S.~Yassemi} [J. Algebra 270, No. 1, 169--180 (2003; Zbl 1032.13014)] and \textit{D.~Anderson, A.~Frazier, A.~Lauve} and \textit{S.~Livingston} [Lect. Notes Pure Appl. Math. 220, 61--72 (2001; Zbl 1035.13004)], respectively.
Belshoff, Richard, Chapman, Jeremy
openaire   +1 more source

GENERALIZATIONS OF THE ZERO-DIVISOR GRAPH

International Electronic Journal of Algebra, 2020
Summary: Let \(R\) be a commutative ring with \(1\neq 0\) and \(Z(R)\) its set of zerodivisors. The zero-divisor graph of \(R\) is the (simple) graph \(\Gamma \)(R) with vertices \(Z(R) \backslash \{0\}\), and distinct vertices \(x\)and \(y\) are adjacent if and only if \(xy= 0\).
ANDERSON, David F., MCCLURKİN, Grace
openaire   +4 more sources