Background on the Geometry on Graphs project

From CanisiusmathWiki

Inventing and Exploring Infinite Families of Graphs

This project is directed by Dr. Terry Bisson.

There are many geometric, number theoretic, and algebraic ways of producing graphs; we will investigate these graphs in terms of their incidence and adjacency matrices. When the examples are finite and combinatorial, the algebraic invariants and properties can be calculated using methods from elementary linear algebra. We will look for patterns in the behavior of the invariants, and try to explain these patterns. One of our goals is to develop parametrized families of graphs, and to descibe how various algebraic invariants and properties change with the parameters.

Among the techniques for inventing new examples will be the use of natural operations in categories of graphs. Ways of varying graphs, such as deletion and contraction, may also be investigated. We will give especial attention to examples related to Cayley graphs and coverings of graphs.

Previous topics include