On a diameter bound for Cayley graphs generated by transposition trees

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 This paper has been withdrawn and a new version with these results and further extensions is at abs/1111.3114