The diameter of the nil-clean graph ofZn

LetRbe a ring with identity. An elementrwas called to be nil-clean ifrwas a sum ofan idempotent and a nilpotent element inR. The nil-clean graph ofRwas a simple graph, denoted byGNC(R), whose vertex set wasR, where two distinct verticesxandywere adjacent if, and only if,x+ywas a nil-clean element ofR. In the absence of the condition that vertexxis not the same asy, thegraph defined in the same way was called the closed nil-clean graph ofR, which may contain loops,and was denoted byGNC(R). In this short note, we completely determine the diameter ofGNC(Zn)