Results 21 to 30 of about 7,874 (214)
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 +2 more sources
Dynamic multi‐objective optimisation of complex networks based on evolutionary computation
IET Networks, EarlyView., 2022 Abstract As the problems concerning the number of information to be optimised is increasing, the optimisation level is getting higher, the target information is more diversified, and the algorithms are becoming more complex; the traditional algorithms such as particle swarm and differential evolution are far from being able to deal with this situation ...
Linfeng Huang
wiley +1 more source
Distributive lattices and some related topologies in comparison with zero-divisor graphs [PDF]
Categories and General Algebraic Structures with Applications, 2021 In this paper,for a distributive lattice $\mathcal L$, we study and compare some lattice theoretic features of $\mathcal L$ and topological properties of the Stone spaces ${\rm Spec}(\mathcal L)$ and ${\rm Max}(\mathcal L)$ with the corresponding graph ...
Saeid Bagheri, mahtab Koohi Kerahroodi
doaj +1 more source
Comments on the Clique Number of Zero-Divisor Graphs of Zn
Journal of Mathematics, 2022 In 2008, J. Skowronek-kazio´w extended the study of the clique number ωGZn to the zero-divisor graph of the ring Zn, but their result was imperfect. In this paper, we reconsider ωGZn of the ring Zn and give some counterexamples. We propose a constructive
Yanzhao Tian, Lixiang Li
doaj +1 more source
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
THE ZERO-DIVISOR GRAPHS OF RINGS AND SEMIRINGS [PDF]
International Journal of Algebra and Computation, 2012 In this paper we study zero-divisor graphs of rings and semirings. We show that all zero-divisor graphs of (possibly noncommutative) semirings are connected and have diameter less than or equal to 3. We characterize all acyclic zero-divisor graphs of semirings and prove that in the case zero-divisor graphs are cyclic, their girths are less than or ...
David Dolzan, Polona Oblak
openaire +1 more source
On a New Extension of the Zero-Divisor Graph [PDF]
Algebra Colloquium, 2020 In this paper, we introduce a new graph whose vertices are the non-zero zero-divisors of a commutative ring R, and for distincts elements x and y in the set Z(R)* of the non-zero zero-divisors of R, x and y are adjacent if and only if xy = 0 or x + y ∈ Z(R).
Cherrabi, A. +3 more
openaire +2 more sources
On graphs with equal coprime index and clique number
AKCE International Journal of Graphs and Combinatorics, 2023 Recently, Katre et al. introduced the concept of the coprime index of a graph. They asked to characterize the graphs for which the coprime index is the same as the clique number. In this paper, we partially solve this problem.
Chetan Patil +2 more
doaj +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
STRUCTURE OF ZERO-DIVISOR GRAPHS ASSOCIATED TO RING OF INTEGER MODULO n [PDF]
Journal of Algebraic Systems, 2023 For a commutative ring $R$ with identity $1\neq 0$, let $Z^{*}(R)=Z(R)\setminus \lbrace 0\rbrace$ be the set of non-zero zero-divisors of $R$, where $Z(R)$ is the set of all zero-divisors of $R$.
Shariefuddin Pirzada +2 more
doaj +1 more source