Question 5 - Cayle Trees

Cayley trees are trees that have a central node, and all the nodes in the tree have degree \(k\). Each time we expand this tree, each leaf connects to another (k-1) node.

A Cayley tree is denoted by P (distance from the leaf to the central node) and k (the degree of any node). The tree in the picture is a P(3) and k(4) Cayley Tree. How many leaf nodes this tree has? For a Cayley Tree with P(\(\delta\)) and k(\(\lambda\)), how many leaf nodes it has?

1. Leaves in the given tree: \(36\) and leaves in the P(\(\delta\)) and k(\(\lambda\)) tree: \(\lambda(\lambda - 1)^{\delta}\)
2. Leaves in the given tree: \(36\) and leaves in the P(\(\delta\)) and k(\(\lambda\)) tree: \(\lambda(\lambda - 1)^{(\delta - 1)}\)
3. Leaves in the given tree: \(42\) and leaves in the P(\(\delta\)) and k(\(\lambda\)) tree: \(\lambda(\lambda)^{(\delta - 1)}\)
4. Leaves in the given tree: \(42\) and leaves in the P(\(\delta\)) and k(\(\lambda\)) tree: \(\lambda(\lambda - 1)^{(\delta - 1)}\)
5. None of the above.

  Original idea by: Pedro Henrique Di Francia Rosso