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!

Apr 17, 10am CT

Speaker: Lord Kavi

Affiliation: Concordia University of Edmonton, Canada

Title: Towards Haemers Laplacian Toughness Conjecture

Abstract: Graph toughness, introduced by Chvátal in 1973, is a key measure of how well different parts of a graph are connected, with implications for Hamiltonicity, spanning trees, connectivity, and more. We derive new bounds on graph toughness and confirm specific cases of a Laplacian-based toughness conjecture by Haemers. Our results include confirmations for regular bipartite graphs, trees, graphs with at least one leaf, graphs with up to 8 vertices, and some specially constructed examples.

No preprint  |  This talk will be recorded  |  You may email the speaker for their slides

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: TBA

Abstract: 

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.