Réunion d'hiver SMC 2026
Montréal, 11 - 14 décembre 2026
Org: Karen Meagher et Hermie Monterde (University of Regina)
[PDF]
- LUDOVICK BOUTHAT, University of Delaware and University of Regina
- STEVE BUTLER, Iowa State University
Gluing via block similarity matrices for distance matrices [PDF]
- STEVE BUTLER, Iowa State University
-
A common method to form cospectral graphs is to glue two graphs on a common vertex. The justification is often carried out by the use of combinatorial interpretations of coefficients of characteristic polynomials that can be readily computed using sparseness of the related matrices. However, if the matrix is dense, e.g. a distance matrix, this approach does not work.
In this talk we will look at how to use block similarity matrices to form cospectral constructions via gluing which work for many classes of matrices, including the adjacency, Laplacian, signless Laplacian, distance, and generalized distance matrix.
This work is the culmination of two REU projects that happened at Iowa State University in recent years.
- HOMER DE VERA, University of Manitoba
- JAIME GARZA, University of Ottawa
- CHRIS GODSIL, University of Waterloo
- KRYSTAL GUO, University of Amsterdam
- MAX LEVIT, York University
- KAREN MEAGHER, University of Regina
- HERMIE MONTERDE, University of Regina
- CALVIN MORIER, York University
- JOY MORRIS, University of Lethbridge
- RAGHU PANTANGI
- JOHNNA PARENTEAU, University of Regina
- SAROBIDY RAZAFIMAHATRATRA, University of Lethbridge
On Ramanujan derangement graphs arising from linear groups of degree two [PDF]
- JAIME GARZA, University of Ottawa
-
Let $X$ be a connected non-bipartite $k$-regular graph on $n$ vertices with eigenvalues $\lambda_1> \lambda_2\geq \ldots\geq \lambda_n$, and let $\lambda(X):=\max\{ |\lambda_2|,|\lambda_n| \}$. The graph $X$ is called a Ramanujan graph if $\lambda(X) \leq 2\sqrt{k-1}$.
Given a finite transitive group $G\leq \operatorname{Sym}(\Omega)$, the derangement graph $\Gamma_G$ is the graph whose vertex set is $G$, and two elements $g$ and $h$ of $G$ are adjacent if $hg^{-1}$ is a derangement, that is, a fixed-point-free permutation. In this talk, we will show that $\Gamma_G$ is a Ramanujan graph for every subgroup $\operatorname{SL}_2(\mathbb{F}_q) \trianglelefteq G\leq \operatorname{GL}_2(\mathbb{F}_q)$ acting transitively on the non-zero vectors of $\mathbb{F}_q^2$ such that $[\operatorname{GL}_2(q):G]$ is odd.
This is based on joint work with Roghayeh Maleki.
- ALIREZA TALEBPOUR, University of Regina
- HARMONY ZHAN, Worcester Polytechnic Institute
- HARMONY ZHAN, Worcester Polytechnic Institute