I was given a graph problem with 3 different questions and 1 set of answers. The problem is described below. The problem that I'm having is that it seems to me that the answer to all the questions is the same. I keep trying to find a caveat but I don't see one. What am I missing?Here is the problemUndirected graph $G$. $n$ - number of vertices. $m$ - number of edges. $d$ - maximum degree of a graph. The maximum clique size of $G$ is no larger than The minimum vertex cover size of $G$ is no larger thanThe maximum independent set size of $\overline{G}$, the complement of $G$, is no larger thanSet of answers(a) $d+1$ (b) $n$(c) $n-1$(d) $n/2$(e) $d$(f) $n-d$It looks to me that the answer to every problem is (b) $n$, becauseClique cannot have more vertices than there are in a graphVertex cover cannot be larger than the number of vertices in a graphMaximum independent set cannot be larger than the number of vertices in a graph. I feel like I'm missing something, because the answers seem too obvious. Any help is appreciated
clique, independent set, and minimum vertex cover
graph theory;graphs