The idempotent graph I(R) of a ring R is a graph with nontrivial idempotents of R as vertices, and two vertices are adjacent in I(R) if and only if their product is zero. In the present paper, we prove that idempotent graphs are weakly perfect. We characterize the rings whose idempotent graphs have connected complements. As an application, the idempotent graph of an abelian Rickart ring R is used to obtain the zero-divisor graph \(\Gamma (R)\) of R.

中文翻译：

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幂等图、弱完美性和零除数图

幂等图形我（ř环的）- [R是具有非平凡幂等的曲线图- [R为顶点，和两个顶点是在相邻的我（[R ）当且仅当他们的产品是零。在本文中，我们证明幂等图是弱完美的。我们描述了其幂等图具有连接互补的环。作为应用，阿贝尔Rickart环的幂等图形ř用于获得零除数图表\（\伽玛（R）\）的- [R 。