Some Properties of the Idempotent Graph of a Ring |
| |
Authors: | H R Dorbidi R Manaviyat S Mirvakili |
| |
Institution: | 1.Department of Basic Sciences,University of Jiroft,Jiroft,Iran;2.Department of Mathematics,Payame Noor University,Tehran,Iran |
| |
Abstract: | 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\({(I(M_n(D))) = 4}\), for all natural number \({n \geq 4}\) and diam\({(I(M_3(D))) = 5}\), 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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|