On the unitary Cayley graphs of group rings

Document Type : Research Paper

Authors

Department of Applied Mathematics and Statistics‎, ‎Faculty of Science and Technology‎,‎ Phetchabun Rajabhat University, Phetchabun‎, ‎Thailand

Abstract

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.

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References

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