DOI
https://doi.org/10.25772/VZQ4-B598
Defense Date
2016
Document Type
Thesis
Degree Name
Master of Science
Department
Mathematical Sciences
First Advisor
Dr. Richard Hammack
Second Advisor
Dr. Dewey Taylor
Third Advisor
Dr. Paul Brooks
Abstract
An n-dimensional halved cube is a graph whose vertices are the binary strings of length n, where two vertices are adjacent if and only if they differ in exactly two positions. It can be regarded as the graph whose vertex set is one partite set of the n-dimensional hypercube, with an edge joining vertices at hamming distance two. In this thesis we compute the automorphism groups of the halved cubes by embedding them in R n and realizing the automorphism group as a subgroup of GLn(R). As an application we show that a halved cube is a circulant graph if and only if its dimension of is at most four.
Rights
Ben MacKinnon
Is Part Of
VCU University Archives
Is Part Of
VCU Theses and Dissertations
Date of Submission
12-14-2016
Included in
Algebra Commons, Discrete Mathematics and Combinatorics Commons, Other Mathematics Commons