University of Manitoba

Zero forcing is a type of graph propagation based on the color-change rule: Given graph $G$, if each vertex of $G$ is colored either white or blue, and vertex $v$ is a blue vertex with only one white neighbor $w$, then change the color of $w$ to blue...

The UManitoba student chapter of the Association for Women in Mathematics (AWM) will be hosting a symposium on November 16, 2023. This hybrid symposium will take place in Armes 205 at the University of Manitoba Fort Garry campus in Winnipeg, Manitoba...

Given a connected undirected graph G = (V,E), where V is the set of vertices and E the set of edges (possibly with weights), denote by A the associated adjacency matrix. The Kemeny constant of the graph G is defined as the Kemeny constant of the...

Kemeny's constant, a fundamental parameter in the theory of Markov chains, has recently received significant attention within the graph theory community. Originally defined for a discrete, finite, time-homogeneous, and irreducible Markov chain based...

In this talk, I will discuss certain extremal configurations in Q-polynomial distance-regular graphs (or P- and Q-polynomial association schemes), which we call descendents. The descendents of a hypercube are precisely its faces. I will show how they...

After a review of n-by-n permutation matrices and n-by-n alternating sign matrices (ASMs), and their relationship, we will discuss the cones that they generate and their Hilbert Bases.

The eccentricity matrix ε(G) of a connected graph G is obtained from the distance matrix of G by keeping the largest nonzero entries in each row and each column, and leaving zeros in the remaining ones. The eigenvalues of ε(G) are the ε-eigenvalues...

We often encounter matrices whose pattern (zero-nonzero, or sign) is known while the precise value of each entry is not clear. Thus, a natural question is what we can say about the spectral property of matrices of a given pattern. When the matrix is...

Graphs having three distinct eigenvalues are a fundamental object of study in spectral graph theory. Strongly regular graphs are the most well-studied examples. In 1995, at the 15th British Combinatorial Conference, Willem Haemers asked do there...

Biological systems often give rise to systems of first order ordinary differential equations (ODEs). Linearization then yields a system x' = Ax, where A is the community matrix. By contrast, mechanical systems often give rise to a second order ODE...