Does Spectral Gap remains same after removal of some edges from a Expander Graph ?
Suppose we take a d-regular graph and remove m edges from it. For a $d$-regular graph We have $\lambda_1 = d$ and $\lambda_2 \leq (1-\epsilon)d $. After removing $m >=0 $ edges, will we have the same spectral gap i.e. $|\lambda_1 - \lambda_2|$ .