hamidreza dorbidi

The idempotent graph of a ring R, denoted by I(R), is a graph whose vertices are all nontrivial idempotents of R and two distinct vertices x and y are adjacent if and only if xy = yx = 0. In this paper, we show that diam(I(Mn(D))) = 4, for all natural number n ≥ 4 and diam(I(M3(D))) = 5, where D is a division ring. We also provide some classes of rings whose idempotent graphs are connected. Moreover, the regularity, clique number and chromatic number of idempotent graphs are studied.