I wanted to clarify if this is possible, so I thought about a possible vertex cover that can also serve as an independent set:
So, to clarify, am I right to say that the nodes in red are both (i) a vertex cover, and (ii) an independent set?
Edit: I was confused by the theorem that states "If
G = (V,E) is a graph, then
S is an independent set <->
V-S is a vertex cover." So I thought that a vertex cover and an independent set are mutually exclusive.