2025 CMS Winter Meeting
Toronto, Dec 5 - 8, 2025
Algebraic Graph Theory: progress and problems
Org: Homer De Vera (University of Manitoba), Chris Godsil (University of Waterloo) and Hermie Monterde (University of Regina)
Org: Homer De Vera (University of Manitoba), Chris Godsil (University of Waterloo) and Hermie Monterde (University of Regina)
- 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
- 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
- MICHAEL CAVERS, University of Toronto Scarborough