  Let $\Gamma$ be a Cayley graph generated by a transposition tree. A natural
problem is to understand how the properties of the Cayley graph depend on those
of the underlying transposition tree. We focus here on diameter and distance
related questions. We examine some related bounds and prove some properties
about them.
  This paper has been withdrawn and a new version with these results and
further extensions is at abs/1111.3114
