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# 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.

Chordal Graph, Chordless Cycle, Cycle Chord

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## References

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

## Cite this as:

Weisstein, Eric W. "Chordless Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ChordlessGraph.html