Answer to Question #307457 in Algebra for deepu

Question

Let T be a tree of order n. Show that the size of the complement T^- of T is the same as the size of K_n-1.

Answer 1

Every tree of order n

n has size n−1

By definition, the complement of a tree on n

n vertices is a graph on n

n vertices and (n2)−(n−1)=(n−12)

(n2)−(n−1)=(n−12) edges. The size of K

n−1Kn−1 is also (n−12)

(n−12)