Let $T$ be a tree with 10 vertices. The sum of the degrees of all the vertices in $T$ is ________

Question

Accepted Answer

Correct answer: 18 — Key facts: For any graph, the sum of degrees of all vertices equals twice the number of edges (Handshake Lemma). For a tree with n vertices, the number of edges is n − 1. Here n = 10, so the number of edges is 10 − 1 = 9. Sum of degrees = 2 × number of edges = 2 × 9 = 18. Therefore, the sum of the degrees of all vertices in the tree is 18.

Let \(T\) be a tree with 10 vertices. The sum of the degrees of all the…