A graph $G=(V,E)$ satisfies $|E| \leq 3 |V| - 6$. The min-degree of $G$ is defined as $ min_{v\in V} \left \{ degree(V) \right \}$. Therefore, min-degree of $G$ cannot be

Given |E| $\le$ 3 |V| -6 We know from graph, Number of edges = $\dfrac{n(n-1)}{2}$ (1) V = 3,                      E = 3                         |3| $\le$ 9 - 6 $\rightarrow$ True (2) V = 4,                      E = 6                         |6| $\le$ 12 - 6 $\rightarrow$ True (3) V = 5,                      E = 10                         |10| $\le$ 15 - 6 $\rightarrow$ notTrue (4) V = 6,                      E = 15                         |15| < |18| - 6 $\rightarrow$ not True So, minimum degree of G cannot be 5