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Pauly Man

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Suppose I have a directed graph in R

Suppose I define an equilibrium point of a directed graph to be a vertex such that I can travel from any adjacent vertex along an edge to that vertex. What is the maximum number of equilibrium points of a directed hypercube in R

As an example in R

(For some reason the graph isn't formatting properly, hopefully you can imagine that it is supposed to be a square).

The upper left corner is an equilibrium point for the directed hypercube.

I now wish to work out how to find the maximum number of equilibrium points possible in a directed hypercube in R

^{n}. Where the graph is a hypercube, (a square in R^{2}, a cube in R^{3}etc).Suppose I define an equilibrium point of a directed graph to be a vertex such that I can travel from any adjacent vertex along an edge to that vertex. What is the maximum number of equilibrium points of a directed hypercube in R

^{n}?As an example in R

^{2}:
Code:

```
*****<*****
* *
^ ^
* *
***** >*****
```

(For some reason the graph isn't formatting properly, hopefully you can imagine that it is supposed to be a square).

The upper left corner is an equilibrium point for the directed hypercube.

I now wish to work out how to find the maximum number of equilibrium points possible in a directed hypercube in R

^{n}. (Any ideas??)
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