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A Graph which is connected (as a Topological Space), i.e., there is a path from any
point to any other point in the Graph. The number of 
-Vertex
(unlabeled) connected graphs for 
, 2, ... are 1, 1, 2, 6, 21, 112, 853, 11117, ... (Sloane's A001349).
References
Chartrand, G. ``Connected Graphs.'' §2.3 in Introductory Graph Theory. New York: Dover, pp. 41-45, 1985.
Sloane, N. J. A. Sequence
A001349/M1657
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.