Let $G=Z_{2}^n$ and $S\subset G$. Is there any relation for number of distinct eigenvalues of $\Gamma=Cayley(G,S)$ graph depending on $n$ and $|S|$ Or at least diameter of $\Gamma$? If you have any hint or references would be appreciated.

Let $G=Z_2^n$ and $S\subset G$. Is there any relation for number of distinct eigenvalues of $\Gamma=Cayley(G,S)$ graph depending on $n$ and $|S|$, or at least diameter of $\Gamma$? If you have any hints or references would be appreciated?

Let $G=Z_{2^n}$ and $S\subset G$. Is there any relation for number of distinct eigenvalues of $\Gamma=Cayley(G,S)$ graph depending on $n$ and $|S|$ Or at least diameter of $\Gamma$? If you have any hint or references would be appreciated.

Let $G=Z_{2}^n$ and $S\subset G$. Is there any relation for number of distinct eigenvalues of $\Gamma=Cayley(G,S)$ graph depending on $n$ and $|S|$ Or at least diameter of $\Gamma$? If you have any hint or references would be appreciated.

Let $G=Z_2^n$ and $S\subset G$. Is there any relation for number of distinct eigenvalues of $\Gamma=Cayley(G,S)$ graph depending on n and $|S|$ Or at least diameter of $\Gamma$? If you have any hint or references would be appreciated?

Let $G=Z_{2^n}$ and $S\subset G$. Is there any relation for number of distinct eigenvalues of $\Gamma=Cayley(G,S)$ graph depending on $n$ and $|S|$ Or at least diameter of $\Gamma$? If you have any hint or references would be appreciated.