91Ó°ÊÓ

a) Let \(F_{1}=\left(V_{2}, E_{1}\right)\) be a forest of seven trees where \(\left|E_{1}\right|=40\). What is \(\left|V_{1}\right|\) ? b) If \(F_{2}=\left(V_{2}, E_{2}\right)\) is a forest with \(\left|V_{2}\right|=62\) and \(\left|E_{2}\right|=51\), how many trees determine \(F_{2}\) ?

a) If \(T\) is a full binary tree of height 5 , how many leaves does \(T\) have? How many internal vertices? How many edges (branches)?b) Answer part (a) for a full binary tree of height \(h\), where \(h \in \mathbf{Z}^{+}\),

a) If a tree has four vertices of degree 2, one vertex of degree 3, two of degree 4, and one of degree 5 , how many pendant vertices does it have? b) If a tree \(T=(V, E)\) has \(v_{2}\) vertices of degree \(2, v_{3}\) vertices of degree \(3, \ldots\), and \(v_{m}\)

a) A complete ternary (or 3 -ary) tree \(T=(V, E)\) has 34 internal vertices. How many edges does \(T\) have? How many leaves? b) How many internal vertices does a complete 5 -ary tree with 817 leaves have?