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Enumeration of Labelled (k, m)-Trees

✍ Scribed by Oleg Pikhurko

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 78 KB
Volume: 86
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1998.2916

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✦ Synopsis

A k-graph is called a (k, m)-tree if it can be obtained from a single edge by consecutively adding edges so that every new edge contains k&m new vertices while its remaining m vertices are covered by an already existing edge. We prove that there are (e(k&m)+m)!(e( k m )&e+1) e&2 e!m!((k&m)!) e distinct vertex labelled (k, m)-trees with e edges.

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Enumeration of Labelled (k,&#xa0;m)-Trees

✦ Synopsis

Enumeration of Labelled (k, m)-Trees