## Information on Graphical Partitions

A graphical partition of order *n* is the
degree sequence
of a graph with *n*/2 edges and no isolated vertices.
For example, when *n* = 6 there are five graphical partitions:
111111, 21111, 2211, 222, 3111. In this case, the five partitions
correspond to the five non-isomorphic graphs on 3 edges
(isolated vertices forbidden), but in general different
graphs could have the same graphical partition.
For *n*=2,4,6,...,30 the number of graphical partitions
is 1, 2, 5, 9, 17, 31, 54, 90, 151, 244, 387, 607, 933, 1420, 2136.
This is sequence
**A000569** in
Neil J. Sloane's
database
of integer sequences.

The program that produces this output is derived from
one kindly supplied to us by Carla Savage. Her program
is based on an algorithm described in the paper:
T.M. Barnes and C.D. Savage,
*Efficient Generation of Graphical Partitions*,
submitted manuscript, 1995.
See also the paper: T.M. Barnes and C.D. Savage,
*A recurrence for counting graphical partitions*,
Electronic Journal of Combinatorics, **2**, 1995, #R11.

Further information can be obtained from Eric Weinstein's
World of Mathematics.

Programs available:

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©Frank Ruskey, 1995-2003.