Question

Two labeled trees are isomorphic if ____________

(a) graphs of the two trees are isomorphic

(b) the two trees have same label

(c) graphs of the two trees are isomorphic and the two trees have the same label

(d) graphs of the two trees are cyclic

I had been asked this question in my homework.

Enquiry is from Properties of Tree in section Trees of Discrete Mathematics

Answer 1

Right option is (c) graphs of the two trees are isomorphic and the two trees have the same label

To explain I would say: The number of labeled trees of k number of vertices is k^n-2. Two labeled trees are isomorphic if their graphs are isomorphic and the corresponding points of the two trees have the same labels.