Subhi Ruzieh, Professor-Assistant, University An Najah, Nablus
"Eigenvalues of Graphs"
The talk is about eigenvalues of graph matrices. We investigate in
particular, the adjacency matrix and the distance matrix. We will
talk about the properties and some bounds on eigenvalues. We look at some
special cases where the eigenvalues are given explicitly. The
concentration will be on complete graphs, complete bi-partite graphs,
cycles, trees and for connected and disconnected graphs.
We check eigenvalues for both the adjacency matrix and the distance matrix
of these graphs. We define coloration and how it may be used to find some
eigenvalues, at least the spectral radius of the matrix.
If time permits, we will talk about graph coloring. This includes
the chromatic index, chromatic polynomial, the number of m-colorings
and some bounds on the chromatic index.