University of Manitoba

The adjugate matrix of a graph G on n vertices, denoted by adj G, is the adjugate of xI - A, where A is the 0-1 adjacency matrix of the graph. The entries of this matrix are polynomials in the variable x, of varying degrees. We shall first outline...

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 1986, Wilf posed the following question ``Which graphs have eigenvectors with entries solely -1 and +1?''. Stevanovic (2016) showed that the problem of finding such graphs is NP-Hard. Caputo, Khames, and Knippel (2019) described all graphs whose...

We study the existence of quantum state transfer on double subdivided star, which is obtained by joining the coalescence vertices of a pair of subdivided stars. Using the Galois group of the characteristic polynomial of a double subdivided star, we...

In this seminar we recall the spectral partitioning method based on a Fiedler vector, i.e., an eigenvector corresponding to the second smallest eigenvalue of the Laplacian matrix of a graph. This problem corresponds to the minimization of a quadratic...

There has been extensive study of diagonalization of matrices, or finding the Jordan Canonical Form for a matrix that is not diagonalizable. Diagonalization can be viewed as using a similarity to concentrate the magnitude of all the entries with a...

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...