A GRAPH WITH RESPECT TO IDEMPOTENT ELEMENTS OF A RING

Let R be a ring with nonzero identity. The Idempotent graph of R, denoted by G Id (R), has its set of vertices equal to the set of all elements of R; distinct vertices x and y are adjacent if and only if x + y is an idempotent of R. In this paper, we study some basic properties of G Id (R) such as connectedness, diameter.