Enumeration of Unigraphical Partitions

Michael D. Hirschhorn, James A. Sellers

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Article number08.4.6
JournalJournal of Integer Sequences
Issue number4
StatePublished - Oct 18 2008
Externally publishedYes


  • Degree sequence
  • Generating function
  • Graph
  • Partition
  • Unigraphical


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