Eight students will participate in the Research Experiences for Undergraduates project aimed at algebraic studies in graph theory. Two advisors will work with the students on topics such as line graphs and their regularity properties which develop when iterated. Work will also be done in determining which graph operations commute with the line graph operator. Other students will consider the classification of graphs whose adjacency matrices have integer eigenvalues, Hamiltonian graphs which arise as joins of other graphs and determinants of distance matrices of unicyclic graphs. Included in the orientation phase, students will be introduced to the program MATLAB, a computer program particularly useful for the computational aspects of linear algebra. A full schedule of invited speakers is planned. In addition, students will be be encouraged to present the results of their work at meetings of the honorary, Pi Mu Epsilon, or those of the Mathematical Association of America.
