When Graphs Share Eigenvectors
Date:
Abstract: Eigenvectors of graph-associated matrices like the Laplacian, adjacency, and variations of them often appear in graph-based applications. From spectral clustering of data to spectral-based redistricting algorithms, eigenvectors prove to be a useful tool.
In this talk, we will discuss a combinatorial perspective on the relationship between graph perturbation and eigenvectors. For various graph operations, we will discuss what conditions are required for two graphs to share eigenvectors. Moreover, the classification of these types of graphs will be shown. We will conclude with avenues for future work.