Problem
COM-B1-M09-P022 Tree with Degrees \(1\) and \(3\)
#22
★★★★☆ Level 4 of 5
A tree has \(12\) vertices, and every vertex has degree either \(1\) or \(3\). How many leaves does it have?
Let \(L\) be the number of leaves and \(T\) the number of degree \(3\) vertices.
Let \(L\) be the number of leaves and \(T\) the number of degree \(3\) vertices. Then \(L+T=12\). The tree has \(11\) edges, so the degree sum is \(22\). Hence \(L+3T=22\). Subtracting the first equation gives \(2T=10\), so \(T=5\) and \(L=7\).
Combines trees with the handshaking formula.