The numbers of claw-free simple graphs on nodes for , 2, ... are 1, 2, 4, 10, 26, 85, 302, 1285, 6170, ... (OEIS
A086991; illustrated above).

The numbers of claw-free connected simple graphs on nodes for , 2, ... are 1, 1, 2, 5, 14, 50, 191, 881, 4494, 26389, 184749,
1728403, ... (OEIS A022562; illustrated above).

Minty (1980) showed that the maximum independent set problem, which is in general NP-complete
on an unrestricted graph, can be solved in strongly polynomial time on a claw-free
graph. His proof used the algorithm of Edmonds (1965) to find the maximum weighted
matching. However, Nakamura and Tamura (2001) showed that this algorithm fails in
some special cases and provided modifications to correct this error. The problem
of finding the independent set of maximum cardinality in a claw-free graph was solved
by Sbihi (1980).

Edmonds, J. "Paths, Trees, and Flowers." Canad. J. Math.17, 449-467, 1965.Faudree, R.; Flandrin, E.; and
Ryjáček, Z. "Claw-Free Graphs--A Survey." Disc. Math.164,
87-147, 1997.Minty, G. J. "On Maximal Independent Sets of
Vertices in Claw Free Graphs." J. Combin. Th. B28, 284-304, 1980.Nakamura,
D. and Tamura, A. "A Revision of Minty's Algorithm for Finding a Maximum Weight
Stable Set of a Claw-Free Graph." J. Oper. Res. Soc. Japan44,
194-204, 2001.Sbihi, N. "Algorithme de Recherche d'un Stable de
Cardinalite Maximum dans un Graphe sans Étoile." Disc. Math.29,
53-76, 1980.Sloane, N. J. A. Sequences A022562
and A086991 in "The On-Line Encyclopedia
of Integer Sequences."