Algebraic Graph Theory: Various Maximum Nullities Associated with a Graph

Talk by Shaun Fallat.

Given a graph, we associate a collection of (typically symmetric) matrices S whose pattern of non-zero entries off of the main diagonal respects the edges in the graph. To this set, we let M denote the maximum possible nullity over all matrices in S. Depending on the choice of the set S, and the family of graphs considered, the parameter M often corresponds to an interesting combinatorial characteristic (planarity, connectivity, coverings, etc.) of the underlying graph.
In this talk, I will survey a number of maximum nullity parameters and highlight some interesting connections and applications to certain aspects of a graph and related implications to an inverse eigenvalue problem for graphs.