Réunion d'hiver SMC 2025
Toronto, 5 - 8 decembre 2025
Théorie algébrique des graphes : progrès et problèmes
Org: Homer De Vera (University of Manitoba), Chris Godsil (University of Waterloo) et Hermie Monterde (University of Regina)
[PDF]
Org: Homer De Vera (University of Manitoba), Chris Godsil (University of Waterloo) et Hermie Monterde (University of Regina)
[PDF]
- JANE BREEN, Ontario Tech University
- STEVE BUTLER, Iowa State University
Cospectral constructions for the $q$-Laplacian matrix [PDF]
- STEVE BUTLER, Iowa State University
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Given a graph we consider the q-Laplacian matrix described as $qD+A$ where $D$ is the diagonal matrix of degrees and $A$ is the adjacency matrix. By proper selection of $q$ we recover well known matrices ($q=0$ is the adjacency; $q=1$ is the signless Laplacian; $q=-1$ is, up to sign, the Laplacian).
It is known that there are graphs which are cospectral (same multiset of eigenvalues) for the $q$-Laplacian for arbitrary choice of $q$ (any regular cospectral pair suffices, but regularity is not needed). The goal of this talk is to highlight some pair of graphs which are cospectral for the $q$-Laplacian for only some specific values of $q$ and we show there are infinitely many values of which have a cospectral pair. One of our tools we will use is some generalization of Godsil-McKay switching.
- JOHN BYRNE, University of Delaware
- MICHAEL CAVERS, University of Toronto Scarborough
- ADA CHAN, York University
- HOMER DE VERA, University of Manitoba
- CHRIS GODSIL, University of Waterloo
- HIMANSHU GUPTA, University of Regina
- ZILIN JIANG, Arizona State University
- SOOYEONG KIM, University of Guelph
- STEVE KIRKLAND, University of Manitoba
- HITESH KUMAR, Simon Fraser University
- ALICA LACAZE-MASMONTEIL, University of Regina
- WILLIAM MARTIN, Worcester Polytechnic Institute
- BOBBY MIRAFTAB, Carleton University
- HERMIE MONTERDE, University of Regina
- JOY MORRIS, University of Lethbridge
A new measure of EKR-robustness on permutation groups [PDF]
- MICHAEL CAVERS, University of Toronto Scarborough
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One of many questions that arises naturally out of extensions of the Erd\H{o}s-Ko-Rado Theorem, is the question of how many edges must be removed from a graph before the independence number increases. We study a variation on this question. The derangement graph of a permutation group is the Cayley graph on that group, whose connection set consists of all of the derangements in the group. Since we are dealing with Cayley graphs, rather than considering all subgraphs that can be produced by removing edges, we instead consider only subgraphs that are still Cayley graphs on the original group: that is, that can be produced by removing inverse-closed sets of elements (derangements) from the original connection set.
This is joint work with Karen Gunderson, Karen Meagher, Venkata Raghu Tej Pantangi, and Mahsa N. Shirazi.
- PIETRO PAPARELLA, University of Washington - Bothell
- JOHNNA PARENTEAU, University of Regina
- SHIVARAM PRAGADA, Simon Fraser University
- MARIIA SOBCHUK, University of Waterloo
- TINO TAMON, Clarkson University
- JOHN URSCHEL, Massachusetts Institute of Technology
- MERI ZAIMI, Université de Montreal
- HARMONY ZHAN, Worcester Polytechnic Institute
- JOHNNA PARENTEAU, University of Regina