Let $G=(V,E)$ be a connected graph with $|E|=17$ and for all vertices $\deg(v)>3$. What is the maximum value of $|V|$? Let $G=(V,E)$ be a connected graph with $|E|=17$ and for all vertices $\deg(v)>3$. What is the maximum value of $|V|$? (What is the maximum possible number of vertices?)

HINT: Suppose that $V=\{v_1,\dots,v_n\}$. Then $$\sum_{k=1}^n\deg(v_k)=34\;;\tag{1}$$ why? 
If $\deg(v_k)\ge 4$ for $k=1,\dots,n$, then $$\sum_{k=1}^n\deg(v_k)\ge\sum_{k=1}^n4\;.\tag{2}$$ Now combine $(1)$ and $(2)$.
