Enumeration of Unigraphical Partitions
Michael D. Hirschhorn
School of Mathematics
James A. Sellers
Department of Mathematics
The Pennsylvania State University
University Park, PA 16802
In the early 1960s, S. L. Hakimi proved necessary and sufficient
conditions for a given sequence of positive integers
d1, d2, ...,
to be the degree sequence of a unique graph (that is, one and only
one graph realization exists for such a degree sequence). Our goal in
this note is to utilize Hakimi's characterization to prove a closed
formula for the function duni(2 m),
the number of "unigraphical partitions" with degree sum 2m.
Full version: pdf,
(Concerned with sequences
Received September 6 2008;
revised version received October 8 2008.
Published in Journal of Integer Sequences, October 18 2008.
Journal of Integer Sequences home page