I know that by drawing it out there is only 1 non-isomorphic tree with 3 vertices, which I got correctly. However, I presume that there is also 1 non-isomorphic binary tree. This is where I am wrong. Why is the answer not 1?
[Math] How many non-isomorphic binary trees can you make with 3 vertices
discrete mathematicstrees
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Best Answer
Binary trees are usually rooted. If isomorphisms are required to map roots to roots, there are two distinct rooted trees with three vertices (both are binary).
Binary trees may also be ordered: each node may have a left child, a right child, both, or neither. Depending on your definition of isomorphism, isomorphisms might be restricted to map left children to left children and right children to right children. In this case there are five distinct binary trees.