Comments on the Clique Number of Zero‐Divisor Graphs of Zn

Y Tian, L Li - Journal of Mathematics, 2022 - Wiley Online Library
In 2008, J. Skowronek‐kazi o´ w extended the study of the clique number ω (G (Zn)) to the
zero‐divisor graph of the ring Zn, but their result was imperfect. In this paper, we reconsider …

On the spectrum of the zero-divisor graphs

Z Barati, M Afkhami… - Asian-European Journal of …, 2022 - World Scientific
Let R be a commutative ring with nonzero identity and Z (R)∗ be the set of all nonzero zero-
divisors of R. The zero-divisor graph of R, denoted by Γ (R), is a simple graph whose vertex …

Rings whose associated extended zero-divisor graphs are complemented

D Bennis, BE Alaoui, R L'hamri - arXiv preprint arXiv:2305.10280, 2023 - arxiv.org
Let $ R $ be a commutative ring with identity $1\neq 0$. In this paper, we continue the study
started in [10] concerning when the extended zero-divisor graph of $ R $, $\overline …

The -extended zero-divisor graphs of idealizations

D Bennis, BE Alaoui, R L'hamri - Journal of Algebra and Its …, 2024 - World Scientific
Let R be a commutative ring with zero-divisors Z (R) and i be a positive integer. The i-
extended zero-divisor graph of R, denoted by Γ¯ i (R), is the (simple) graph with vertex set Z …