Final answer:
An n-vertex tree in mathematics refers to a tree graph with 'n' vertices, and it will always have zero faces, therefore we can't assign a length to something inexistent. Any two vertices in the tree are connected by exactly one path, and there are no cycles.
Step-by-step explanation:
In graph theory, a tree is an acyclic connected graph. Because a tree can't have any cycles, it doesn't have any 'faces' in the traditional sense of a polyhedron. So, the number of faces in an n-vertex tree is zero. As a result, we can't assign a length to the faces since they do not exist.
The term 'n-vertex tree' usually refers to a tree graph consisting of 'n' vertices (nodes). In a tree, any two vertices are connected by exactly one path, and there are no cycles.
A key property of trees is that they always have 'n-1' edges if there are 'n' vertices. This is known as a tree property and can be proven using mathematical induction.
Learn more about Tree Graph