Title: Controllable graphs
|Affiliation:||University of Waterloo|
Abstract: A graph is controllable if no eigenvector is orthogonal to the all-ones vector. O’Rourke and Touri proved that almost all graphs are controllable. Consequences of this are proofs that almost all graphs are asymmetric, that almost all graphs are vertex reconstructible and that almost all graphs do not admit perfect state transfer. I will present proofs of some of these consequences.
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