Suppose I have a directed graph in R(adsbygoogle = window.adsbygoogle || []).push({}); ^{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}:

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

*****<*****

* *

^ ^

* *

***** >*****

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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# Equilibrium Points of Directed Graphs

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