A chordal graph is a simple graph in which every graph cycle of length four and greater has a cycle chord. In other words, a chordal graph is a graph possessing no chordless cycles.
The numbers of simple chordal graphs on n = 1, 2, 3, 4, … nodes are 1, 2, 4, 10, 27, 94, 393, …
The first few are illustrated below, though many are trivially chordal since they possess no cycles of length ≥4.
