A Meyniel graph, also called a very strongly perfect graph, is a graph in which every odd cycle of length five or more has at least two chords. Meyniel graphs are perfect.
The numbers of connected Meyniel graphs on 
, 2, ... verticea are 1, 1, 2, 6, 19, 88, 459, 3060, 23989,
... (the first few of which are illustrated above), and the corresponding numbers
of not-necessarily connected Meyniel graphs are 1, 2, 4, 11, 32, 130, 622, 3839,
... (OEIS A123434).
By definition, any graph with no odd cycle of length 
is trivially Meyniel. Classes of graphs that are Meyniel
include empty graphs (trivially), complete
graphs, and trees (trivially).
