A short proof of Cayley's Tree Formula

Details A short proof of Cayley's Tree Formula A short proof of Cayley's Tree Formula

2009-08-17

arxiv.org/abs/0908.2324v2

Mathematics

Combinatorics

3 pages, 1 figures;Removed 'Introduction' and 'Appendix';Rearranged the text to make it more compact

Scientific paper

A simple combinatorial argument employing symmetry of edges is put forth to establish a recursive relation for counting the number of different labeled trees $T_n$ on $n$ vertices. $T_n = \frac{n}{2} \sum_{k=0}^{n-2} {n-2 \choose k} T_{k+1} T_{n-k-1};$ for n > 1 and $T_1 = 1$ It is proved that $T_n$ calculated from this recursive relation is equivalent to the well known Cayley's Tree Formula $n^{n-2}$.

Affiliated with

Also associated with

No associations

Rating

A short proof of Cayley's Tree Formula does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A short proof of Cayley's Tree Formula, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A short proof of Cayley's Tree Formula will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-19426