University of Manitoba

A sign pattern (matrix) has entries in {+, -, 0}. We investigate eigenvalue properties of a sign pattern of order 2n where two of the blocks are prescribed sign patterns of order n, and the other two (order n) blocks are the positive diagonal sign...

The distance matrix of a graph records the length of the shortest path between any two vertices. Graham and Pollak found that when the underlying graph is a tree, the determinant of the distance matrix satisfies a nice, simple formula. In particular...

In this talk, I will introduce group-invariant quantum latin squares and their connection to quantum isomorphisms. There will be some representation theory and finally, we will see a method of constructing Cayley graphs that are quantum isomorphic...

Zero forcing is a combinatorial game played on a graph with the ultimate goal of changing the colour of all the vertices at a minimal cost. Originally this game was conceived as a one-player game, but later a two-player version was devised in...

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...