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
Recommended Citation
Bhoumik, Soumya, "On the Automorphism Groups of Almost All Circulant Graphs and Digraphs" (2013). Theses and Dissertations. 3363.
https://scholarsjunction.msstate.edu/td/3363
Comments
Nor- mal||Small||GRR||DRR||Asymptotic automorphism group||Cayley (di)graph||Non-normal Circulants