The non-nilpotent graph of a semigroup Vrije Universiteit Brussel
(called the upper non-nilpotent graph of $S$). The vertices of
this graph are the elements of $S$ and two vertices are adjacent
if they generate a semigroup that is not nilpotent (in the sense
of Malcev). In case $S$ is a group this graph has been introduced
by A. Abdollahi and M. Zarrin and some remarkable properties have
been proved. The aim of ...