摘要

Let R be a ring with identity. The unitary Cayley graph of R is the simple graph with vertex set R, where two distinct vertices x and y are linked by an edge if and only if x - y is a unit of R. A graph is said to be planar if it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In this paper, we completely characterize the rings whose unitary Cayley graphs are planar.