A chordless graph is a simple graph possessing no chords.
A chordal graph (which possesses no chordless cycles) is not the same as (or converse of) a chordless graph (which possesses no chords).
For example, the square graph 
is chordless but not chordal,
the diamond graph and tetrahedral
graph 
are chordal but not chordless, and empty
graphs 
,
path graphs 
, and the triangle graph 
are both chordal
and chordless.
The numbers of connected simple chordless graphs on 
, 2, ... nodes are 1, 1, 2, 4, 10, 27, ... (OEIS A287693),
the first few of which are illustrated above.
The numbers of not-necessarily connected simple chordless graphs on 
, 2, ... nodes are 1, 2, 4, 9, 21, 56, ... (OEIS A287694),
the first few of which are illustrated above.
