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.

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REFERENCES

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

مواضيع ذات صلة

Minimum Spanning Tree

Maximum Leaf Number

Lobster Graph

Labeled Tree

Internal Path Length

Red-Black Tree

Pseudotree

Pseudoforest

Prüfer Code

Planted Tree

Planted Planar Tree

Graph Strength