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

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