Theses and Dissertations

Issuing Body

Mississippi State University

Advisor

Dobson, Edward T.

Committee Member

Johnson, Corlis P.

Committee Member

Smith, Robert C.

Committee Member

Woodroofe, Russell

Committee Member

Miller, T. Len

Date of Degree

8-17-2013

Document Type

Dissertation - Open Access

Major

Mathematical Sciences

Degree Name

Doctor of Philosophy

College

College of Arts and Sciences

Department

Department of Mathematics and Statistics

Abstract

We attempt to determine the structure of the automorphism group of a generic circulant graph. We first show that almost all circulant graphs have automorphism groups as small as possible. Dobson has conjectured that almost all of the remaining circulant (di)graphs (those whose automorphism groups are not as small as possible) are normal circulant (di)graphs. We show this conjecture is not true in general, but is true if we consider only those circulant (di)graphs whose orders are in a “large” subset of integers. We note that all non-normal circulant (di)graphs can be classified into two natural classes (generalized wreath products, and deleted wreath type), and show that neither of these classes contains almost every non-normal circulant digraph.

URI

https://hdl.handle.net/11668/21131

Comments

Nor- mal||Small||GRR||DRR||Asymptotic automorphism group||Cayley (di)graph||Non-normal Circulants

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