DOI
https://doi.org/10.25772/1YSV-A333
Defense Date
2010
Document Type
Thesis
Degree Name
Master of Science
Department
Mathematical Sciences
First Advisor
Richard Hammack
Abstract
This thesis generalizes to digraphs certain recent results about graphs. There are special digraphs C such that AxC is isomorphic to BxC for some pair of distinct digraphs A and B. Lovasz named these digraphs C zero-divisors and completely characterized their structure. Knowing that all directed cycles are zero-divisors, we focus on the following problem: Given any directed cycle D and any digraph A, enumerate all digraphs B such that AxD is isomorphic to BxD. From our result for cycles, we generalize to an arbitrary zero-divisor C, developing upper and lower bounds for the collection of digraphs B satisfying AxC isomorphic to BxC.
Rights
© The Author
Is Part Of
VCU University Archives
Is Part Of
VCU Theses and Dissertations
Date of Submission
May 2010