0 votes 0 votes DS tree + – Shivangi Parashar 2 asked Aug 28, 2018 recategorized Jun 13, 2022 by Arjun Shivangi Parashar 2 478 views answer comment Share Follow See all 5 Comments See all 5 5 Comments reply srestha commented Aug 28, 2018 reply Follow Share incomplete question which tree binary tree? 0 votes 0 votes Shaik Masthan commented Aug 28, 2018 reply Follow Share @Shivangi Parashar 2 this may help you https://gateoverflow.in/230861/tree-ds 0 votes 0 votes ankitgupta.1729 commented Aug 29, 2018 reply Follow Share Answer should be (B) According to Cayley's Formula :- Total Number of possible trees with 'n' labeled nodes = $n^{n-2}$ , $n\geq2$ It can be proved by Prufer Sequences. 0 votes 0 votes Shaik Masthan commented Aug 29, 2018 reply Follow Share @ankitgupta.1729 brother, in the question they didn't mention that it is binary tree ===> you took an arbitrary tree right? 0 votes 0 votes ankitgupta.1729 commented Aug 29, 2018 reply Follow Share Sir, In question, it is asked about a tree, not a binary tree. binary tree is rooted and ordered. It is a well-known Cayley's formula to find total number of possible trees if vertices are labeled. In case of rooted trees , this formula becomes $n^{n-2} * n = n^{n-1}$ because any of the n vertices can be selected as a root. I am attaching the screenshot from the Graph Theory book by Narsingh Deo. PFA. https://en.wikipedia.org/wiki/Cayley's_formula 1 votes 1 votes Please log in or register to add a comment.