## 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
Anum=A000569">
**A000569** in

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:

It was last updated .