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Abstract
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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.
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