“Extremal EIgenvalues
of Graphs”

Türker Bıyıkoğlu

(Işık University)

Abstract: The
fundamental graph properties e.g. coloring, diameter, isomorphism and connectivity are
closely related (or bounded) to the eigenvalues
of matrix representations of these graphs (e.g. adjacency matrix or
Laplacian matrix of the graph). The sharp eigenvalue bounds for such graph invariants depend on the extremal

eigenvalues. Extremal graph
eigenvalue problem is finding a graph in a given
graph class that has the minimum (or maximum) eigenvalue for a given matrix representation.

I shall talk
about these connections between graph properties and eigenvalues
of graphs. I shall present results, methods, difficulties and possible further
research topics on extremal graph eigenvalue problems. This talk is intended for general audience.
No specialist knowledge is required.

Date : April 16, 2010 (Friday)

Time : 13.40-14.30

Place: Seminar Room SA-141