A New Upper Bound for the Diameter of the Cayley Graph of a Symmetric Group

Author

Hangwei ZhuangFollow

Date Thesis Awarded

5-2018

Access Type

Honors Thesis -- Access Restricted On-Campus Only

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Gexin Yu

Committee Members

Junping Shi

Deborah C. Bebout

Abstract

Given a finite symmetric group S_n and a set S of generators, we can represent the group as a Cayley graph. The diameter of the Cayley graph is the largest distance from the identity to any other elements. We work on the conjecture that the diameter of the Cayley graph of a finite symmetric group S_n with S ={(12),(12...n)} is at most $ C(n,2). Our main result is to show that the diameter of the graph of S_n is at most (3n^2-4n)/2.

Recommended Citation

Zhuang, Hangwei, "A New Upper Bound for the Diameter of the Cayley Graph of a Symmetric Group" (2018). Undergraduate Honors Theses. William & Mary. Paper 1193.
https://scholarworks.wm.edu/honorstheses/1193