Defense Date


Document Type


Degree Name

Master of Science


Mathematical Sciences

First Advisor

Richard Hammack


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.


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Date of Submission

May 2010