Abstract:
There are many ways to calculate the characteristic
polynomial of a directed graph. I will describe the Figure
Equation, which provides a direct link between a graph's
structure and the coefficients of the characteristic
polynomial of its adjacency matrix. Using the figure
equation and combinatorics on disjoint cycles, I will show
how to calculate the characteristic polynomial of some
graphs at sight and prove recursion patterns for some
families of graphs. I will relate this approach to graph
coverings and derivatives.
This talk, which will include background and
original results about graphs and matrices, is based on work
at the summer 2006 REU at Canisius.