Hydra game

Rules

1. There are Rooted graphs a. Every node has a single parent node b. Leaf is a node which is furthest with only one edge to its parent
2. Pick a leaf x
3. Pick an integer n
4. Remove x
5. Add a new n branches to x’s grandparent

Example

We consider the following rooted graph with root 1 and 3 branches from 1 $\to$ [2 3 4 ] Then from each [2 3 4] 3 more branches as shown in the Fig Hydra head