Consider the question:
Given a (simple undirected) graph $G$, at most how many vertices can we select, such that every two of them don't share any common neighbors?
My teacher asked this question with the hypercube version ($G$ is the hypercube graph), where he mentioned the name "unit sphere packing" (which is more or less accurate and figurative). (The hypercube version can be easily solved by considering the regularity of the graph and $|G|/|N[v]|$.)
Is there any study of "unit sphere packing" of more general graphs?
I don't know of a name, or results about this, but you can describe the problem as follows:
For a graph $G=(V,E)$, compute the the maximal independent set of the graph $G' = (V,E')$, where $E' = \{\{v,w\}\in\binom{V}{2}\ |\ N_G(v)\cap N_G(w) = \emptyset \}$.
So you can translate the problem quite literally to: "take as many as possible vertices that are not adjacent in the graph where adjacency means that they have a common neighbour in the original graph".