On a diameter bound for Cayley graphs generated by transposition trees

TL;DR

This paper investigates how the diameter of Cayley graphs generated by transposition trees relates to the properties of the underlying trees, providing bounds and properties, although the original paper has been withdrawn for revisions.

Contribution

It introduces bounds and properties connecting transposition tree structures to the diameter of their Cayley graphs, advancing understanding of their combinatorial properties.

Findings

Derived bounds for Cayley graph diameters

Proved properties relating transposition trees to graph metrics

Enhanced understanding of transposition-generated Cayley graphs

Abstract

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 This paper has been withdrawn and a new version with these results and further extensions is at abs/1111.3114