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.