USRA Seminar - Chen Xie

Title: Controllable Graphs Determined by their Generalized Spectrums

Abstract: 

A graph G is controllable if its walk matrix $W = \{ 1 A1 (A^2)1
... (A^(n-1))1\}$ is invertible. G is determined by its generalized
spectrum if for any graph H, G and H are cospectral with cospectral
complements implies that G and H are isomorphic. We derive some exclusion conditions on the arithmetic properties of the walk matrix, and show that for all controllable graphs G whose walk matrix W satisfy $\det(W) \2^\floor{n/2}$ is an odd square-free integer, G is determined by its generalized spectrum.