GATE CS 2017 Set 1 Q20 — Trees

According to the fundamental properties of trees and graph theory:

1. A tree $T$ with $n$ vertices always has exactly $e = n - 1$ edges.
2. By the Handshaking Lemma, the sum of the degrees of all vertices in any graph is equal to twice the number of edges:
   $$\sum_{v \in V} \text{deg}(v) = 2e$$

Given that the tree $T$ has $n = 10$ vertices:

• Number of edges, $e = 10 - 1 = 9$
• Sum of degrees $= 2 \times 9 = 18$