Prove Theorem 12 6 and Corollary 12 1 Theorem 12 6 Let T (V, E) be a complete m ary tree with V n If T has i leaves and i internal vertices, then (a) n mi 1 (b) (m 1)i 1 and (c) i ( 1) (m 1) (n 1) m Corollary 12 1 Let T be a balanced complete m ary tree with i leaves Then the height of T is logm ...

Theorem 126 a Each internal vertex has m children so there are mi vertices that ar ...

Prove Theorem 12.6 and Corollary 12.1. Theorem 12.6 Let T = (V, E) be a complete m-ary

Question:

Prove Theorem 12.6 and Corollary 12.1.
Theorem 12.6
Let T = (V, E) be a complete m-ary tree with |V| = n. If T has i leaves and i internal vertices, then
(a) n = mi + 1;
(b) ℓ = (m - 1)i + 1; and
(c) i = (ℓ - 1)/(m - 1) = (n - 1)/m.
Corollary 12.1.
Let T be a balanced complete m-ary tree with i leaves. Then the height of T is ⌈logm ℓ⌉.