Research Projects
(Brief Descriptions, 2007)
Minimum Semidefinite Rank of a Graph, directed by Dr. Sivaram Narayan
We explore the minimum semidefinite rank of certain matrices associated with finite graphs. This rank depends on certain geometric properties of the graph and also depends on whether the underlying field is real or complex. This exploration involves a rich area of matrix analysis. Read more....
Geometric Labelings of Graphs, directed by Dr. Sivaram Narayan
This new research project explores a particular type of vertex labeling of a graph. There are many types of graph vertex labelings; this is an area of active research in graph theory. In this project, we focus on constructing multiplicative vertex labelings that are (a,r)-geometric. Read more....
Statistical Modeling of the El Ni–o/La Ni–a Phenomena, directed by Dr. John Daniels
This research project will attempt to build an effective model to evaluate the effect of El Ni–o/La Ni–a phenomena on microclimates. We will begin with simple linear regression models and then use a variety of enhancement techniques to find a model of the climate data. Eventually the model will be extended to a number of additional climate metrics. Read more....
Distance regular Cayley graphs, directed by Dr. Ken Smith
A Cayley graph is a graph with vertices labeled by elements of a finite group; the adjacency relations of the graph are preserved by the action of this group on the vertices. In this project we study Cayley graphs of nonabelian groups, concentrating on graphs which are distance regular with small diameter. Read more....
Cyclic Difference Sets, directed by Dr. Ken Smith
This project examines difference sets in cyclic groups. Using group theory, representations of groups as sets of matrices and some elementary algebraic number theory, we tackle parameters of difference sets where the existence of cyclic difference sets is open. Read more....
Last updated February 26, 2007