Line graph of extensions of the zero-divisor graph in commutative rings

• Date: 2025
• Main Authors: Rehman, Nadeem ur, Mir, Shabir Ahmad, Nazim, Mohd
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2025
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/7817
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 512.6 We consider a finite commutative ring with unity denoted by $\mathscr{P}.$ Within this framework, the essential graph of $\mathscr{P}$ is represented as $E{G}(\mathscr{P})$ with $Z(\mathscr{P})^* = Z(\mathscr{P})\setminus\{0\}$ as the vertex set, and two distinct vertices $x$ and $y$ are a...