trees

Let $$G$$ $$\,\,\,\,\, = \,\,\,\left( {V,\,\,\,\,\,E} \right)$$ be a graph. Define $$\xi \left( G \right) = \sum\limits_d {{i_d} \times } {\mkern 1mu} d,$$ where $${{i_d}}$$ is the...

In a complete k-ary tree, every internal node has exactly k children. The number of leaves in such a tree with n internal nodes is

What is the maximum number of edges in an acyclic undirected graph with $$n$$ vertices?

The number of leaf nodes in a rooted tree of n nodes, with each node having 0 or 3 children is:

A complete n-ary tree is one in which every node has O or n sons. If x is the number of internal nodes of a complete n-ary tree, the number of leaves in it is given by