A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called
the root of the graph. The rooted graphs on nodes are isomorphic with the symmetric
relations on
nodes. The counting polynomial for the number of rooted graphs with points is

Cameron, P. J. "Sequences Realized by Oligomorphic Permutation Groups." J. Integer Seqs.3, #00.1.5, 2000.Harary,
F. Graph
Theory. Reading, MA: Addison-Wesley, p. 186, 1994.Harary,
F. and Palmer, E. M. Graphical
Enumeration. New York: Academic Press, p. 241, 1973.Harary,
F.; Palmer, E. M.; Robinson, R. W.; and Schwenk, A. J. "Enumeration
of Graphs with Signed Points and Lines." J. Graph Theory1, 295-308,
1977.McIlroy, M. D. "Calculation of Numbers of Structures
of Relations on Finite Sets." Massachusetts Institute of Technology, Research
Laboratory of Electronics, Quarterly Progress Reports. No. 17, Sept. 15,
pp. 14-22, 1955.Oberschelp, W. "Kombinatorische Anzahlbestimmungen
in Relationen." Math. Ann.174, 53-78, 1967.Sloane,
N. J. A. Sequences A000666/M1650
and A070166 in "The On-Line Encyclopedia
of Integer Sequences."