University of Guilan Journal of Algebra and Related Topics 2345-3931 14 Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024). 2026 04 01 On the unitary Cayley graphs of group rings 247 255 9525 10.22124/jart.2026.28297.1705 EN K. Limkul Department of Applied Mathematics and Statistics‎, ‎Faculty of Science and Technology‎,‎ Phetchabun Rajabhat University, Phetchabun‎, ‎Thailand S. Nanta Department of Applied Mathematics and Statistics‎, ‎Faculty of Science and Technology‎,‎ Phetchabun Rajabhat University, Phetchabun‎, ‎Thailand Journal Article 2024 09 01 Let $R$ be a ring. The unitary Cayley graph of a ring $R$, denoted by $\Gamma(R)$, is a graph with vertex set $R$ where two vertices $u,v\in R$ are adjacent if and only if $u-v$ is a unit of $R$. In this paper, we investigate the unitary Cayley graph of a finite ring, called a group ring, and examine its fundamental properties. We present the conditions for adjacency, the connectivity of the graph and its basic structure. Additionally, we provide the exact value of the degree of a vertex and the distance between any two vertices within the graph. https://jart.guilan.ac.ir/article_9525_9b5c4422dd7362b6f2fb357bc67f160b.pdf