  The enhanced power graph of a finite group is the graph whose vertex set is
the set of the elements of this group, and two distinct vertices are adjacent
if they generate a cyclic subgroup. In this paper, we classify all finite
groups whose enhanced power graphs are split graphs and threshold graphs. We
also classify all finite nilpotent groups whose enhanced power graphs are
chordal graphs and Cographs. Finally, we give some families of non-nilpotent
groups whose enhanced power graphs are chordal graphs and Cographs. The results
partly answer a question was posed by Peter J. Cameron.
