Chordless Graph

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.

REFERENCES

Sloane, N. J. A. Sequences A287693 and A287694 in "The On-Line Encyclopedia of Integer Sequences."