University of Manitoba

In combinatorial matrix theory (CMT) one studies properties of combinatorial matrices, i.e., matrices with entries 0, 1 and -1. For instance, permutation matrices, i.e., (0,1)-matrices with exactly one 1 in every row and column, are interesting...

Many quantum search algorithms are equivalent to coined quantum walks that start from a uniform superposition of arcs and get very close to a state that "concentrates on" some marked vertex. In this talk, we consider a related problem: if we start...

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...