University of Manitoba

In this talk I will present several eigenvalue bounds on the independence number and the distance chromatic number of graph powers. We will see how to use polynomials and mixed-integer linear programming in order to optimize such bounds. Some...

Let G be a connected simple graph and L be its Laplacian matrix. Let v be a cut vertex and B be a branch at v. Assume that v_1 is the only vertex in B adjacent to v. Let P be a path that starts at v_1 and stays inside B. It is shown that the...

Suppose Alice can send a quantum message to Bob in a quantum system modeled as a finite graph. But, imagine there is an eavesdropper which can attach an infinite-dimensional quantum system to the finite graph used by Alice and Bob. Can Alice still...

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...

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...

We first review some known results about resistance matrix of an undirected graph. We then define resistance distance in a strongly connected, directed graph. When the graph is balanced, that is, the indegree and the outdegree of any vertex are the...

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...

The adjacency matrix A of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. If u and v are distinct vertices in G, we say perfect state transfer from u to v occurs if there is a time t such that the (u,v)-entry of...

Let G be a simple connected graph and A(G) be its adjacency matrix. A nonsingular graph G is said to have the reciprocal eigenvalue property if the reciprocal of each eigenvalue of G is also an eigenvalue. Furthermore, if each eigenvalue of G and its...

Math Academy for incoming Indigenous Nursing Students. We will be working on basic skills to get them ready for their math course which starts in September.