Algebraic Graph Theory Seminar - Judi McDonald

Monday, August 9, 2021 11:30 am - 11:30 am EDT (GMT -04:00)

Title: Skew Adjacency Matrices:  The Number of Characteristic polynomials of Skew Cacti

Speaker: Judi McDonald
Affiliation: Washington State University
Zoom: Contact Soffia Arnadottir


In this talk, I will begin by reviewing the Harry-Sachs method for finding the characteristic polynomial of a matrix with a given digraph, as well as a couple of useful variations.  Then I will illustrate how we (JMcD, Matt Hudelson, Amy Streifel) used this technique to explore the number of different characteristic polynomials that can be achieved by skew adjacency matrices of a given graph.  If G = (VE) is a graph with V = {1, 2, …, n}, then an nxmatrix A is a skew adjacency matrix of G provided ajk = 0 whenever {jk} is not in E, and |ajk| = 1, with ajkakj  = -1, whenever {j,k} is in E