Let $G$ be a graph. Use the Handshake Theorem to prove that $\delta(G)\nu(G) \le 2\varepsilon(G) \le \Delta(G)\nu(G)$.
So the first step to solve this I know is that you need to know what everything stands for, like
- $\delta(G)$= minimum degree
- $\nu(G)$ number vertices,
- $\varepsilon(G)$ number edges, and
- $\Delta(G)$ = maximum degree $G$.
Then I know we use the formula $d(G) = 2\varepsilon (G)$. But this is where I get lost because I do not know how to apply the theorem. Any tips regarding how to solve this enigma would be kindly appreciated.