The subset of vertices in a graph is called "non-disturbing" if any two vertices from this subset could be connected by a path not passing through other vertices of this subset.
Informally speaking, any two members must have a way to speak to each other without disturbing other members.
And we want to put as many members in a graph as we could.
My question is:
Is an algorithm known for building largest non-disturbing subset of a graph?
I'm especially interested in solving this task for
n-dimensional hypercube (having
n is from 1 to 64.
By paper-and-pencil approach I could find solutions for small
n=1 we could have 2 members,
n=2 we could have 3 members,
n=3 we could have 5 members,
n=4 we could have 10 members.
But I doubt that, for example, the case
n=16 would be brute-forcible.