In the early 1960s, S. L. Hakimi proved necessary and sufficient conditions for a given sequence of positive integers d1, d2,..., dn 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(2m), the number of "unigraphical partitions" with degree sum 2m.
|Original language||English (US)|
|Journal||Journal of Integer Sequences|
|State||Published - Oct 18 2008|
- Degree sequence
- Generating function