On the genus of the annhilator graph of a commutative ring

• Date: 2018
• Main Authors: Tamizh Chelvam, T., Selvakumar, K.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: commutative ring; annihilator graph; genus; planar; local rings; 05C99; 05C15; 13A99
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/79
• Journal Title: Algebra and Discrete Mathematics

Let \(R\) be a commutative ring and \(Z(R)^*\) be its set of non-zero zero-divisors. The annihilator graph of a commutative ring \(R\) is the simple undirected graph \(\operatorname{AG}(R)\) with vertices \(Z(R)^*\), and two distinct vertices \(x\) and \(y\) are adjacent if and only if \(\operatorna...