Let R be a ring with nonzero identity. The Idempotent graph of R, denoted by GId(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 GId(R) such as connectedness, diameter and girth.

中文翻译：

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关于环的幂等的图

让R是一个非零标识的环。这幂等图的R，表示为GID(R), 其顶点集等于所有元素的集R; 不同的顶点X和是的相邻当且仅当X + 是的是幂等的R. 在本文中，我们研究了一些基本属性GID(R)例如连通性、直径和周长。