Calculating the average degree/valency of vertices

Question

If I were to let T be a tree with n vertices, what would be the average degree/valency of the vertices in T? How would I go about calculating this?

Answer 1

Hints:

(i) How many edges does a tree on $n$ vertices have?

(ii) Each edge of a graph contributes $2$ to the total degree sum of the graph.

This allows you to calculate the total degree sum for a tree on $n$ vertices, and from this you can find the average degree.

Answer 2

If you know the definition of degree of a vertex in a graph, then you can easily calculate the average valency of a tree.

If $K$ is the average valency, then we have $$K=\frac{1}{n}(\deg(v_1)+\deg(v_2)+\ldots+\deg(v_n)),$$ where $n$ is the total number of vertices in a tree, $\deg(v_1)$ is the degree(valency) of $v_1$ (first vertex) and so on.