The enhanced power graph 
of a finite group 
is the simple
graph with vertex set 
in which distinct elements 
and 
are adjacent iff
they generate a cyclic group (Aalipour et al.
2017). Equivalently, they must belong to a common cyclic subgroup.
In the ordinary power graph, adjacency instead requires one of 
and 
to be a power of the other.
If 
is a cyclic group, then 
is a complete graph.
For a noncyclic elementary Abelian group,
the maximal cliques are the subgroups
of prime order. Distinct such subgroups
meet only at the identity element.
Manna (2026, p. 1) classified the finite simple groups whose enhanced power graphs are chordal.
They are the cyclic groups of prime order,
the alternating group 
, the projective
special linear groups 
for 
and 
, and the Suzuki
groups 
for 
.
