• 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.