Let $S_n$ denote the symmetric group on $n$ letters. If we consider the Cayley graph $\Gamma(S_n,C)$, where $C=\{(12),(12\cdots n)\}$, is there any formula for calculating the diameter of $\Gamma(S_n,C)$?
In fact, for an example, I need to know the diameter of this Cayley graph for big numbers, e.g. $n=100$ or $n=1000$.