Degree Sequence
Given an undirected Graph, a degree sequence is a monotonic nonincreasing sequence of thedegrees of its Vertices. A degree sequence is said to be 
-connected if there exists some-Connected Graph corresponding to the degree sequence. For example, while the degree sequence 
is1- but not 2-connected, 
is 2-connected. The number of degree sequences for 
, 2, ... is given by 1,2, 4, 11, 31, 102, ... (Sloane's A004251).
References
Ruskey, F. ``Information on Degree Sequences.'' http://sue.csc.uvic.ca/~cos/inf/nump/DegreeSequences.html. Ruskey, F.; Cohen, R.; Eades, P.; and Scott, A. ``Alley CATs in Search of Good Homes.'' Congres. Numer. 102, 97-110, 1994. Sloane, N. J. A. SequenceA004251/M1250in ``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.