Defense Date


Document Type


Degree Name

Master of Science


Mathematical Sciences

First Advisor

Dr. Richard Hammack

Second Advisor

Dr. Dewey Taylor

Third Advisor

Dr. Paul Brooks


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.


Ben MacKinnon

Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission