In 1990, Grimaldi defined a graph based on the elements and units of the ring of integers modulo n. The vertices of this graph are the elements of $Z_n$; distinct vertices $x$ and $y$ are defined to be adjacent if and only if $x+y$ is a unit of $Z_n$. Recently a generalization of the unit graph is defined and studied for an arbitrary ring with nonzero identity. In this talk, we are going to study the unit graphs of the rings of polynomials and power series and compare some invariants of $G(R)$, $G(R[x])$ and $G(R[[x]])$. Also, we present some slight generalizations of some of the previous gained results in this context.
