Enumeration of Unigraphical Partitions

Michael D. Hirschhorn; James Allen Sellers

Enumeration of Unigraphical Partitions

Michael D. Hirschhorn, James Allen Sellers

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In the early 1960s, S. L. Hakimi proved necessary and sufficient conditions for a given sequence of positive integers d₁, d₂,..., d_n 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 d_uni(2m), the number of "unigraphical partitions" with degree sum 2m.

Original language	English (US)
Article number	08.4.6
Journal	Journal of Integer Sequences
Volume	11
Issue number	4
State	Published - Oct 18 2008

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

Cite this

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abstract = "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.",

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AB - 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.

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Enumeration of Unigraphical Partitions

Abstract

All Science Journal Classification (ASJC) codes

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