05C50 Online

05C50 Online is a biweekly virtual seminar about graphs and matrices held on a Friday, 10AM Central Time via Zoom. This is organized by Stephen Kirkland (University of Manitoba), Hermie Monterde (University of Regina) and Homer de Vera (University of Manitoba). Kindly fill out THIS FORM to subscribe to our mailing list!

May 1, 10am CT

Speaker: Sarojini Mohapatra

Affiliation: NIT Rourkela, India

Title: Pair state transfer on graphs with isomorphic branches

Abstract: In this talk, we discuss pair state transfer on graphs with respect to the adjacency matrix. We show that the evolution of certain pair states in a quantum network with isomorphic branches depends solely on the local structure, and it remains unaffected even if the global structure is altered. Furthermore, all graphs that enable high-fidelity vertex state transfer can be considered as isomorphic branches of a quantum network to exhibit high-fidelity pair state transfer. This result provides a framework for constructing infinite families of graphs, such as trees and unicyclic graphs, that exhibit perfect pair state transfer. In particular, we characterize the existence of pair state transfer in various graphs, including paths and cycles.

Preprint  |  This talk will NOT be recorded  |  Slides will be shared

May 15, 10am CT

Speaker: Domingos Cardoso

Affiliation: University of Aveiro, Portugal

Title: Graphs whose least eigenvalue does not change after deleting the neighborhood of any vertex

Abstract: During the Aveiro Workshop on Graph Spectra 2006, in its Problems Session, the author proposed the AWGS.13 problem (Graphs with stable least eigenvalue) which appears in [D. Stevanovic, Research problems from the Aveiro Workshop on Graph Spectra, Linear Algebra Appli. 423 (2007): 172--181]. This problem consists of finding a characterization of the graphs G satisfying the property that its least eigenvalue does not change after deleting the neighborhood of any vertex. I recently realized that, as far as I know, there hasn't been a single published attempt to solve this problem in the last twenty years. The goal of this presentation is to call the attention for this problem, introducing some related results using Cauchy's interlacing inequalities and the theory of star sets and star complements.

No preprint  |  This talk will be recorded  |  Slides will be shared

For titles and abstracts of previous talks, and links to recordings, please visit here .

Please contact Hermie Monterde  if you have inquiries about the seminar.