Defense Date

2012

Document Type

Thesis

Degree Name

Master of Science

Department

Mathematical Sciences

First Advisor

Richard Hammack

Second Advisor

Ghidewon Abay-Asmerom

Third Advisor

Dewey Taylor

Fourth Advisor

George Munro

Abstract

There are four prominent product graphs in graph theory: Cartesian, strong, direct, and lexicographic. Of these four product graphs, the lexicographic product graph is the least studied. Lexicographic products are not commutative but still have some interesting properties. This paper begins with basic definitions of graph theory, including the definition of a graph, that are needed to understand theorems and proofs that come later. The paper then discusses the lexicographic product of digraphs, denoted $G \circ H$, for some digraphs $G$ and $H$. The paper concludes by proving a cancellation property for the lexicographic product of digraphs $G$, $H$, $A$, and $B$: if $G \circ H \cong A \circ B$ and $|V(G)| = |V(A)|$, then $G \cong A$. It also proves additional cancellation properties for lexicographic product digraphs and the author hopes the final result will provide further insight into tournaments.

Rights

© The Author

Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

December 2012

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