Solution
= Solution
If $Av=\lambda v$, choose $i$ with $|v_i|$ maximal. Then $|\lambda||v_i|=|\sum_{j\sim i}v_j|\le d(i)|v_i|\le\Delta|v_i|$, so $|\lambda|\le\Delta$.
= Solution
If $Av=\lambda v$, choose $i$ with $|v_i|$ maximal. Then $|\lambda||v_i|=|\sum_{j\sim i}v_j|\le d(i)|v_i|\le\Delta|v_i|$, so $|\lambda|\le\Delta$.