GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
88 views
number of distinct binary tree,that can be created by 5 nodes(distinct)
asked in Graph Theory by Veteran (18.2k points)   | 88 views

1 Answer

0 votes
$5$ distinct nodes means you can uniquely identify each node based on some parameter say a key value, Then the solution to this problem is given by bell's number.

Number of binary trees possible $= \binom {2n}{n}*n!$
answered by Boss (8.6k points)  
Could you please elaborate this solution numerically?

I think its not correct.

#unlabelled binary trees possible = nth catalan number

Now, being labelled , they cn be permuted in n! ways.

So, answer = $\frac{\binom{2n}{n}}{n+1} * n!$

Correct me if wrong.

Bell no. gives partitions. It doesnt consider permutations.

Related questions

0 votes
2 answers
1
0 votes
0 answers
2
Top Users Feb 2017
  1. Arjun

    5386 Points

  2. Bikram

    4230 Points

  3. Habibkhan

    3952 Points

  4. Aboveallplayer

    3086 Points

  5. Debashish Deka

    2564 Points

  6. sriv_shubham

    2318 Points

  7. Smriti012

    2236 Points

  8. Arnabi

    2008 Points

  9. mcjoshi

    1696 Points

  10. sh!va

    1684 Points

Monthly Topper: Rs. 500 gift card

20,863 questions
26,021 answers
59,689 comments
22,131 users