The diameter of the nil-clean graph of Zn.

Let R be a ring with identity. An element r was called to be nil-clean if r was a sum of an idempotent and a nilpotent element in R. The nil-clean graph of R was a simple graph, denoted by G_NC(R), whose vertex set was R, where two distinct vertices x and y were adjacent if, and only if, x + y was a nil-clean element of R. In the absence of the condition that vertex x is not the same as y, the graph defined in the same way was called the closed nil-clean graph of R, which may contain loops, and was denoted by GNC(R). In this short note, we completely determine the diameter of G_NC(Z_n). [ABSTRACT FROM AUTHOR]