The edge chromatic number of \(\Gamma_{I}(R)\)

• Date: 2018
• Main Authors: Kala, R., Mallika, A., Selvakumar, K.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: zero-divisor graph; chromatic number; ideal-based zero-divisor graph; 05C99; 13A15; 13F10
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/76
• Journal Title: Algebra and Discrete Mathematics

For a commutative ring \(R\) and an ideal \(I\) of \(R\), the ideal-based zero-divisor graph is the undirected graph \(\Gamma_{I}(R)\) with vertices \(\{x\in R-I: xy\in I~ \text{for some}~ y\in R-I\}\), where distinct vertices \(x\) and \(y\) are adjacent if and only if \(xy\in I\). In this paper, w...