Let Rbe a finite commutative ring with nonzero identity. The Vnr-graph of R, denoted by  has its set of vertices equal to  the set of all elements of R; distinct vertices xand yare adjacent if and only if xyis a Von Neumann regular element of R. In this article, the basic properties of  are investigated and some characterization results regarding connectedness, diameter, girth and planarity of  are given.

connectedness, diameter, girth, planarity, Vnr-graph, Von Neumann regular ring.