DOI
https://doi.org/10.25772/CNFS-ZJ21
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