pretty thingUoP maths seminar (2013-14)

Some results on graphs and matrix spectra.

Speaker: Murad Banaji

Venue: Wednesday 12th March 2014, 2pm, LG2.04a (refreshments provided)

Abstract: Algebraic graph theory involves deducing properties of graphs from algebraic objects - e.g. matrices, polynomials, groups - associated with the graphs. A result may go: "if a graph G has spectral property Γ, then it belongs to class G". Alternatively, we may be more interested in a linear algebraic question, but pass to graphs to help answer it. For example, we may deduce that all matrices associated with certain graphs have certain spectral properties. I'll present a couple of recent neat equivalences in this direction. The results take the form: "a graph G belongs to class G if and only if all matrices in class M(G) have propery M". This includes slightly unexpected characterisations of two well-studied classes of graphs, trees and caterpillars. The results are inspired by certain applications in dynamical systems.